REVISED  EDITION 


THE 


AMERICAN 


DESIGNED 


FOR  THE  USE  OF  SCHOOLS  AND  ACADEMIES; 


CONTAINING 

AN  EXTENSIVE  COLLECTION  OF  PRACTICAL  QUESTIONS,  WITH 
CONCISE  AND  ORIGINAL  METHODS  OF  SOLUTION,  WHICH 
SIMPLIFY  MANY  OF  THE  MOST  IMPORTANT 
RULES  IN  WRITTEN  ARITHMETIC. 


BY 

JOHN  F.  STODDARD,  A.M., 

AUTHOR  OF  “THE  JUVENILE  MENTAL,”  “THE  PRACTICAL,”  AND  “THE 
PHILOSOPHICAL  ARITHMETIC,”  “THE  ELEMENTARY,”  AND 
“THE  UNIVERSITY  ALGEBRA,”  “KEYS,”  ETC. 


NEW  YORK: 

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»  CINCINNATI  :  APPLEGATE  A  CO.  CLEVELAND :  INGHAM  &  BRAGG. 

DETROIT:  PUTNAM,  SMITH  A  CO.  CHICAGO:  VV.  B.  KEEN. 

AND  ALL  BOOKSELLERS. 


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NORMAL  MATHEMATICAL  SERIES. 


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Entered,  according  to  an  Act  of  Congress,  in  the  year  1849,  by 
JOHN  F.  STODDARD 

In  the  Clerk’s  Office  of  the  District  Court  for  the  Southern  District  of 

New  York. 


Entered,  according  to  an  Act  of  Congress,  in  the  year  1860,  by 
SHELDON  &  COMPANY, 

In  the  Clerk’s  Office  of  the  District  Court  for  the  Southern  District  of 

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Electrotyped  by  Smith  &  McDougal,  No.  84  Beekman-st.,  N.  Y. 


K  Hohn 


t 


I  $  (a  0 

\ 


PREFACE. 


Neither  a  desire  of  pecuniary  gain,  nor  a  wish  to 
appear  as  an  author,  prompted  the  presentation  of 
this  work  to  the  public.  Having  felt  the  necessity 
of  a  more  extended  and  systematic  Intellectual 
Arithmetic  for  the  younger,  as  well  as  more  ad¬ 
vanced  pupils,  I  prepared  and  used  in  manuscript, 
in  my  own  school,  for  a  number  of  years,  such  a 
series  of  questions  as  I  deemed  best  adapted  to 
the  purpose.  After  observing  the  superior  mental 
training  derived  from  their  use,  and  the  ease  with 
which  pupils  thus  trained  comprehended  the  more 
advanced  branches  of  mathematics,  I  venture  to 
submit  them  to  the  public  in  the  following  pages, 
hoping  that  they  may  prove  as  useful  to  other 
schools  as  they  have  to  my  own. 

The  rule  which  I  have  observed  in  its  preparation 
is  to  tell  but  one  thing  at  a  time,  and  that  in  its 
proper  place. 

It  would  be  laborious  to  point  out  all  the  particu¬ 
lars  in  which  this  work  differs  from  others  of  a  sim¬ 
ilar  character ;  I  shall,  therefore,  give  only  a  brief 
exposition  of  its  general  plan,  leaving  the  other 
differences  (which,  doubtlessly,  will  be  considered 
of  importance)  to  be  found  by  those  who  study  the 
book. 

Chapters  First,  Second ,  Third ,  and  Fourth ,  treat 
respectively  of  Addition,  Subtraction,  Multiplica- 


iv 


PREPACE. 


tion,  and  Division  of  simple  numbers ;  each  of 
which  is  rendered  familiar  by  an  extensive  col¬ 
lection  of  practical  questions.  The  last  Lesson  in 
Chapter  /Second ,  consists  of  questions,,  which  com¬ 
bine  Addition  and  Subtraction ;  the  last  Lesson  in 
Chapter  Third ,  of  questions  combining  Addition, 
Subtraction,  and  Multiplication.  Thus,  an  intimate 
connection  between  Lessons  and  even  Chapters  is 
kept  up  through  the  entire  work,  with  the  excep¬ 
tion  of  Chapter  Fifth, ,  which  contains  a  few  of  the 
most  important  tables  of  SV eights  and  Measures  ; 
each  of  which  is  illustrated  with  appropriate  ques¬ 
tions. 

Chapter  Sixth  is  devoted  to  the  subject  of 
Fractions,  and  contains  twenty  lessons,  hi  which 
many  oiiginal  combinations  and  concise  solutions 
occur. 

Chapter  Seventh  consists  of  practical  and  in¬ 
tricate  questions  of  various  kinds,  which  require  for 
their  solution  a  thorough  knowledge  of  the  preceding 
Chapters.  This  Chapter  (which,  it  is  believed,  is 
not  contained  in  any  similar  work,)  when  thoroughly 
understood,  will  be  of  incalculable  benefit  to  those 
who  are  studying,  or  intend  to  study  Algebra. 

Chapter  Eighth  includes  Interest,  Discount,  and 
per  cent,  of  every  description,  in  their  various 
modifications.  The  method  of  treating  these  sub¬ 
jects  is  original;  and  renders  the  rules  in  Written 
Ai  ithmetics,  under  these  heads  (which  are  often 
incomprehensible  to  pupils)  perfectly  intelligible  by 
reducing  the  whole  to  one  continued  train  of  rea¬ 
soning. 


PEEFACE. 


V 


It  is  believed  that  this  Chapter,  if  thoroughly 
taught,  can  not  fail  to  quicken,  strengthen  and  de¬ 
velop  the  reasoning  powers  ;  bringing  into  exercise, 
as  it  does,  nearly  every  principle  taught  in  the 
twenty  lessons  of  Chapter  Sixth ,  and  also,  the 
greater  part  of  Chapter  Seventh ,  it  must  of  neces¬ 
sity  cause  the  pupil  to  acquire  the  habit  of  syste¬ 
matically  classifying  his  knowledge,  that  he  may, 
at  any  time,  be  able  to  call  to  his  aid,  such  portions 
of  it  as  will  assist  him  in  illustrating  or  demonstra¬ 
ting  the 

The  mind  is  composed  of  a  variety  of  faculties 
which  require  for  their  development  appropriate 
and  constant  exercise.  That  Intellectual  Arithme¬ 
tic,  when  properly  taught,  is  better  calculated,  than 
any  other  study,  to  invigorate  and  develop  these 
faculties,  to  produce  accurate  and  close  discrimi¬ 
nation,  and,  to  enable  the  pupil  to  acquire  a  knowl¬ 
edge  of  the  Higher  Mathematics  with  greater  ease, 
can  not  for  a  moment  admit  of  a  doubt. 

J.  F.  STODDARD. 

New  York,  August  1,  1860. 


subject  under  consideration. 


SUGGESTIONS  TO  TEACHERS. 


For  the  benefit  of  those  whose  experience  is  limited,  I 
make  the  following  suggestions  in  regard  to  the  most  ap¬ 
proved  methods  of  teaching  this  important  branch  of  study : 

The  lesson  should  be  assigned  previous  to  recitation,  to 
afford  the  pupils  an  opportunity  for  its  examination :  the 
use  of  the  book,  by  pupils,  during  class  exercise,  should  be 
entirely  prohibited. 

To  concentrate  the  attention  of  the  whole  class,  pupils 
should  be  called  upon  promiscuously  to  solve  the  problems, 
and  not  in  rotation,  as  is  too  frequently  the  case. 

No  question  should  be  read  more  than  once,  if  done 
slowly  and  distinctly ;  the  student  should  be  required  to  re¬ 
produce  and  solve  it  without  interruption,  unless  it  be  to 
make  a  necessary  criticism  or  correction. 

Care  should  be  taken  that  the  pupils  (during  recitation) 
assume  an  erect  position,  and  that  the  language  they  use 
be  rigidly  accurate  as  to  construction  and  articulation. 

Pupils,  if  not  carefully  guarded,  will,  in  their  hurried 
solutions,  pronounce  many  of  the  most  simple  words  in¬ 
correctly.  For  instance,  the  words :  and ,  of,  if  for ,  with, 
what,  which,  where ,  when ,  costs,  quarts ,  how  many,  etc.,  are 
not  unfrequently  pronounced  :  an,  off,  ef  fur,  withe,  wat, 
witch,  ware,  wen ,  coss,  quais,  hominy,  etc. 

By  careful  attention  to  all  of  these  particulars,  a  lesson  in 
Intellectual  Arithmetic  is  a  practical  lesson  in  elocution, 
grammar,  rhetoric,  and  logic,  as  well  as  a  lesson  in  the 
science  of  numbers. 

It  is  respectfully  suggested  that  the  particular  forms  given 
for  the  solution  of  questions  be  adhered  to,  unless  better 
ones  should  be  devised  by  the  teacher,  J.  F.  S. 


ARITHMETIC. 


CHAPTER  I. 


LESSON  I. 


1. 

2 

and 

1 

arc 

liow 

many  ? 

Solution. 

— Two  and  one  are  3. 

2. 

2 

and 

2 

are 

how 

many  ? 

3. 

2 

and 

3 

are 

how 

many  ? 

4. 

2 

and 

4 

are 

how 

many  ? 

5. 

2 

and 

5 

are 

how 

many  ? 

6. 

2 

and 

6 

are 

how 

many  ? 

V. 

.2 

and 

7 

are 

how 

many  ? 

8. 

2 

and 

8 

are 

how 

many  ? 

9. 

2 

and 

9 

are 

how 

many  ? 

10. 

3 

and 

2 

are 

how 

many  ? 

11. 

3 

and 

3 

are 

how 

many  ? 

12. 

3 

and 

4 

are 

how 

many  ? 

13. 

3 

and 

5 

are 

how 

many  ? 

14. 

3 

and 

6 

are 

how 

many  ? 

15. 

3 

and 

7 

are 

how 

many  ? 

16. 

3 

and 

8 

are 

how 

many  ? 

17. 

3 

and 

9 

are 

how 

many  ? 

18. 

4 

and 

3 

are 

how 

many  ? 

19. 

4 

and 

4 

are 

how 

many  ? 

20. 

4 

and 

5 

are 

how 

many  ? 

21. 

4 

and 

6 

are 

how 

many  ? 

22. 

4 

and 

7 

are 

how 

many  ? 

23. 

4 

and 

8 

are 

how 

many  ? 

24. 

4 

and 

9 

are 

how 

many  2 

8 


ADDITION. 


25.  James  killed  2  birds  and  John  1  ;  bow  many 
did  both  kill  ? 

Solution. — If  James  killed  2  birds  and  John  1,  they  together 
killed  2  birds  and  1  bird,  which  are  3  birds. 

26.  I  gave  2  cents  to  Henry,  and  2  cents  to  Harvey  ; 
how  many  cents  did  both  receive  ? 

21.  Hiram  had  2  cents,  and  his  brother  gave  him 

3  more ;  how  many  had  he  then  ? 

28.  George  gave  me  2  apples,  and  Mary  gave  me 

4  ;  how  many  did  both  give  me  ? 

29.  A  man  had  2  cows,  and  he  purchased  5  more  ; 
how  many  cows  had  he  then  ? 

30.  John’s  father  gave  him  2  oranges,  and  his 
mother  gave  him  6  ;  how  many  did  he  receive  in  all  ? 

31.  Philo  bought  2  peaches,  and  his  brother  gave 
him  1 ;  how  many  had  he  then  ? 

32.  Philip  gave  me  2  plums,  and  Myron  gave  mo 
8  ;  how  many  did  they  together  give  me  ? 

33.  A  farmer  had  2  horses,  and  bought  9  more  ; 
how  many  had  he  then  ? 

34.  William  had  3  candies,  and  Moses  gave  him  2 
more  ;  how  many  had  he  then  l 

35.  John  bought  3  apples,  and  I  gave  him  3 ;  how 
many  had  he  then  ? 

36.  Philip  gave  3  cents  for  some  nuts,  and  4  cents 
for  some  candies  ;  how  many  cents  did  he  pay  for  both  ? 

3 1.  I  paid  3  cents  for  some  wafers,  and  5  cents  for 
a  stamp ;  how  much  did  both  cost  me  ? 

38.  A  merchant  bought  3  barrels  of  sugar  and  6 
barrels  of  molasses  ;  how  many  barrels  did  he  buy  ? 

39.  Ralph  is  3  years  old,  and  Edward  is  1 ;  what  is 
the  sum  of  their  ages  ? 

40.  A  lemon  cost  3  cents,  and  a  pine-apple  cost  8; 
how  much  did  both  cost  ? 

41.  James  solved  3  questions  in  arithmetic,  and 
Oliver  9  ;  how  many  did  both  solve  ? 


ADDITION. 


9 


42.  If  it  take  4  yards  of  cloth  for  a  coat,  and  3  for 
a  pair  of  j>ants,  how  many  yards  will  it  take  for  both  ? 

43.  Samuel  bought  4  marbles,  and  found  4  ;  how 
many  had  he  then  ? 

44.  Isaac  bought  4  sheets  of  paper,  and  I  gave  him 
5  ;  how  many  had  be  then  ? 

45.  A  mau  bought  a  peck  of  apples  for  4  cents,  and 
a  peck  of  pears  for  6  cents ;  how  much  did  the  apples 
and  pears  together  cost  ? 

46.  If  Mary  has  4  books,  and  her  father  should  give 
her  7,  how  many  books  would  she  then  have  ? 

47.  William  has  4  marbles  in  his  hand,  and  8  in  his 
pocket ;  how  many  has  he  in  all  ? 

48.  Charles  walked  4  miles,  and  rode  9  ;  how  far 
did  he  go  ? 

49.  In  a  certain  class  there  are  5  boys,  and  4  girls  ; 
how  many  pupils  are  there  in  the  class  ? 


LESSON 

II. 

1. 

5 

and 

4 

are 

how 

many  ? 

2. 

5 

and 

5 

are 

how 

many  ? 

3. 

5 

and 

6 

are 

how 

many  ? 

4. 

5 

and 

7 

are 

how 

many  ? 

5. 

5 

and 

8 

are 

how 

many  ? 

6. 

5 

and 

9 

are 

how 

many  ? 

7. 

6 

and 

5 

are 

how 

many  ? 

8. 

6 

and 

6 

are 

how 

many  ? 

9. 

6 

and 

7 

are 

how 

many  ? 

10. 

6 

and 

8 

are 

how 

many  ? 

11. 

6 

and 

9 

are 

how 

many  ? 

12. 

7 

and 

6 

are 

how 

many  ? 

13. 

7 

and 

7 

are 

how 

many  ? 

14. 

7 

and 

8 

are 

how 

many  ? 

15. 

7 

and 

9 

are 

how 

many  ? 

10 


addition. 


16. 

8 

and 

7 

are 

how 

17. 

8 

and 

8 

are 

how 

18. 

8 

and 

9 

are 

how 

19. 

8 

and 

5 

are 

how 

20. 

9 

and 

6 

are 

how 

21. 

9 

and 

8 

are 

how 

22. 

9 

and 

9 

are 

how 

23. 

9 

and 

10 

are 

how 

24. 

9 

and 

7 

are 

how 

25. 

9 

and 

11 

are 

how 

many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 

.  **.”•  IXXIS  answered  o  questions  correctly  and  4 
incorrectly ;  how  many  questions  was  she  asked  ? 

21.  A  beggar  met  two  boys  ;  one  gave  him  5  cents, 
and  the  other  gave  him  G  cents ;  how  many  cents  did 
they  together  give  him  ? 

28.  A  man  bought  a  hat  for  5  dollars,  and  a  pair  of 
boots  for  6  dollars ;  how  much  was  the  cost  of  both  ? 

29.  There  are  9  boys  on  one  bench,  and  8  on  an¬ 
other  ;  how  many  are  there  on  both  ? 

30.  Maria  gave  her  teacher  5  pinks  and  7  roses* 
how  many  flowers  did  she  give  him  ? 

31.  Tlariy  caught  5  squirrels,  and  Henry  cauo-ht  8  * 
how  many  did  both  catch  ? 


32.  If  we  learn  5  pages  this  week,  and  9  next;  how 
many  will  we  learn  in  the  two  weeks  ? 

33.  Frank  sold  a  melon  for  6  cents,  and  an  orange 
lor  5  cents ;  how  many  cents  did  he  receive  for  both  ? 

34.  John  bought  6  whips,  and  Joseph  gave  him  6  * 
how  many  had  he  then  ? 

35.  George  had  6  chestnuts,  and  Richard  gave  him 
7  ;  how  many  had  he  then  ? 

36.  Henry  bought  6  candies,  and  Sarah  bought  8  * 
how  many  were  bought  by  both  ? 

37.  Rebecca  has  G  oranges,  and  Catharine  has  9  * 
how  many  oranges  have  both  ? 

38.  A  boy  bought  7  apples,  and  his  father  gave 
him  6  ;  how  many  had  he  then  ? 


ADDITI ON. 


11 


39.  Minerva  bought  7  yards  of  ribbon,  and  her  mother 
gave  her  7  ;  how  many  yards  did  she  then  have  ? 

40.  There  were  7  boys  sitting  on  one  bench,  and  8 
on  another  ;  how  many  were  there  on  both  ? 

41.  There  were  7  boys  at  play,  and  9  other  boys 
joined  them  ;  how  many  were  there  in  all  ? 

42.  If  I  have  8  cents  in  one  hand,  and  7  cents  in  the 
other,  how  many  have  I  in  both  ? 

43.  If  Mary  has  8  peaches,  and  Margaret  has  9, 
how  many  have  both  ? 

44.  Sally  gave  9  cents  for  some  thread,  and  7  cents 
for  some  needles  ;  how  much  did  the  needles  and  thread 
cost  her  ? 

45.  Charles  has  9  marbles,  and  Albert  has  5  ;  how 
many  marbles  have  Charles  and  Albert  ? 

*  46.  9  birds  were  in  a  tree,  and  6  were  on  the  ground; 

how  many  were  there  in  all  ? 

47.  Sarah  gave  9  cents  for  some  cinnamon,  and 
7  cents  for  some  raisins ;  how  many  cents  did  these 
cost  her  ? 

48.  George  shot  9  pigeons,  and  James  shot  8  ;  how 
many  did  both  shoot? 

49.  Russel  caught  7  fish,  and  Robert  caught  5  ;  how 
many  did  both  catch  ? 

50.  In  one  field  there  are  8  horses,  and  in  another 
there  are  9  ;  how  many  are  there  in  both  ? 

-  - 

LESSON  III. 

1.  How  many  are  10  and  2?  10  and  3  ?  10  and  4  ? 

10  and  5  ?  10  and  6  ?  10  and  7  ?  10  and  9  ?  10  and  8? 
10  and  10  ? 

2.  How  many  are  2  and  2  ?  2  and  12  ?  2  and  22  ? 
2  and  32  ?  2  and  42  ?  2  and  52  ?  2  and  62  ?  2  and 
72  ?  2  and  82  ?  2  and  92  ? 


12 


ADDITION. 


3.  How  many  are  3  and  3  ?  3  and  13  ?  3  and  23  ? 
3  and  33  ?  3  and  43  ?  3  and  53  ?  3  and  63  ?  3  and  *73? 

3  and  83  ?  3  and  93  ?  96  and  4  ? 

4.  How  many  are  4  and  4  ?  4  and  14  ?  4  and  24  ? 

4  and  34  ?  4  and  44  ?  4  and  54  ?  4  and  64  ?  4  and  74  ? 

4  and  84  ?  4  and  94  ?  98  and  2  ? 

5.  How  many  are  5  and  5  ?  5  and  15  ?  5  and  25  ? 

5  and  35  ?  5  and  45  ?  5  and  55  ?  5  and  65  ?  5  and  75  ? 

5  and  85  ?  5  and  95  ? 

6.  How  many  are  6  and  6  ?  6  and  16  ?  6  and  26? 

6  and  36  ?  6  and  46  ?  6  and  56  ?  6  and  66  ?  6  and  76  ? 

6  and  86  ?  6  and  96  ? 

7.  How  many  are  7  and  7  ?  7  and  17  ?  7  and  27  ? 

7  and  37  ?  7  and  47  ?  7  and  57  ?  7  and  67  ?  7  and  77  ? 

7  and  87  ?  7  and  97  ? 

8.  How  many  are  8  and  8  ?  8  and  18  ?  8  and  28  ? 

8  and  38  ?  8  and  48  ?  8  and  58  ?  8  and  68  ?  8  and  78  ? 

8  and  88  ?  8  and  98  ? 

9.  How  many  are  9  and  9  ?  9  and  19  ?  9  and  29  ? 

9  and  39  ?  9  and  49  ?  9  and  59  ?  9  and  69  ?  9  and  79  ? 

9  and  89  ?  9  and  99  ? 

10.  How  many  are  10  and  11  ?  10  and  21  ?  10  and 

31  ?  10  and  41  ?  10  and  51  ?  10  and  61  ?  10  and  71  ? 

10  and  81  ?  10  and  91  ? 

11.  How  many  are  10  and  12  ?  10  and  22  ?  10  and 

32  ?  10  and  42  ?  10  and  52  ?  10  and  62  ?  10  and  72  ? 
10  and  82  ?  10  and  92  ? 

12.  How  many  are  10  and  4?  10  and  14?  10  and 
24  ?  10  and  34?  10  and  44  ?  10  and  54  ?  10  and  64  ? 

10  and  74  ?  10  and  84  ?  10  and  94  ? 

13.  How  many  are  11  and  3  ?  11  and  13  ?  11  and 

23  ?  11  and  33  ?  11  and  43  ?  11  and  53  ?  11  and  63  ? 

11  and  73  ?  11  and  83  ?  11  and  93  ? 

14.  How  many  are  11  and  4  ?  11  and  14  ?  11  and 

24  ?  11  and  34  ?  11  and  44  ?  11  and  54  ?  11  and  64  ? 
11  and  74  ?  11  and  84  ?  11  and  94  ? 

15.  How  many  are  10  and  5  ?  10  and  15  ?  10  and 


ADDITION. 


13 


35  ?  10  and  45  ?  10  and  55  ?  10  and  65  ?  10  and  75  f 

10  and  85  ?  10  and  95  ?  10  and  25  ? 

16.  How  many  are  11  and  5  ?  11  and  15  ?  11  and 
25  ?  11  and  35  ?  11  and  45  ?  11  and  55  ?  11  and  65  ? 

11  and  75  ?  11  and  85  ?  11  and  95  ? 

17.  How  many  are  3  and  8  ?  3  and  18  ?  3  and  28  ? 

3  and  38  ?  3  and  48  ?  3  and  58  ?  3  and  68  ?  3  and  78? ; 
3  and  88  ?  3  and  98  ? 

18.  How  many  are  8  and  4  ?  8  and  14  ?  8  and  24  ? 

8  and  34  ?  8  and  44  ?  8  and  54  ?  8  and  64  ?  8  and  74  ? 

8  and  84  ?  8  and  94  ? 

19.  How  many  are  7  and  5  ?  7  and  17  ?  7  and  27  ? 

7  and  37  ?  7  and  47  ?  7  and  57  ?  7  and  67  ?  7  and  77  ? 

7  and  87  ?  7  and  97  ? 

20.  How  many  are  8  and  6  ?  8  and  16  ?  8  and  26  ? 

8  and  36  ?  8  and  46  ?  8  and  56  ?  8  and  66  ?  8  and 
76  ?  8  and  86  ?  8  and  96  ? 


LESSON  IV, 


1. 

8 

and 

9 

arc 

how 

many? 

2. 

11 

and 

7 

are 

how 

many  ? 

3. 

10 

and 

9 

are 

how 

many  ? 

4. 

7 

and 

14 

are 

how 

many  ? 

5. 

6 

and 

12 

are 

how 

many  ? 

6. 

9 

and 

15 

are 

how 

many  ? 

7. 

11 

#nd 

18 

are 

how 

many  ? 

8. 

15 

and 

12 

are 

how 

many  ? 

9. 

14 

and 

13 

are 

how 

many  ? 

10. 

16 

and 

14 

are 

how 

many  ? 

11. 

21 

and 

12 

are 

how 

many  ? 

12. 

24 

and 

13 

are 

how 

many  ? 

13. 

25 

and 

15 

are 

how 

many  % 

14. 

27 

and 

13 

are 

how 

many  ? 

15. 

23 

and 

17  %re 

2 

how 

many  ? 

14 


ADDITION. 


16. 

29 

and 

11 

are 

how 

many  ? 

17. 

30 

and 

20 

are 

how 

many  ? 

18. 

34 

and 

15 

are 

how 

many  ? 

19. 

32 

and 

18 

are 

how 

many  ? 

Remark. — The  symbol  =  is  the  sign  of  equality ,  and  when 
placed  between  two  quantities  it  denotes  that  they  are  equal  to 
each  other.  Thus  10  cents  =  1  dime,  is  read,  10  cents  equal 
1  dime. 

The  symbol  + ,  is  called  plus ;  and  denotes  that  the  quanti¬ 
ties  between  which  it  is  placed,  are  to  be  added.  Thus,  4  +  2 
= 6,  shows  that  4  and  2  are  to  be  added :  and  is  read,  four 
plus  two  equals  6. 

20.  33  +  44  are  how  many  ? 

21.  35  +  15  are  how  many  ? 

22.  36  +  12  are  how  many? 

23.  40  +  36  are  how  many? 

24.  40  +  29  are  how  many? 

25.  44  +  20  are  how  many  ? 

26.  48  +  32  are  how  many? 

27.  45  +  35  are  how  many? 

28.  4  +  8  +  6  are  how  many? 

29.  8  +  2  +  7  are  how  many  ? 

30.  10  +  7  +  3  are  how  many  ? 

31.  12  +  10  +  9  are  how  many  ? 

32.  15  + 12  +  6  are  how  many  ? 

33.  18  +  4  +  10  are  how  many  ? 

34.  24  +  16  +  12  are  how  many? 

35.  22  +  33  +  11  are  how  many? 

36.  15  +  16  +  2  are  how  many? 

37.  28  +  12  +  15  are  how  many  ? 

38.  46  +  24  +  19  are  how  many  ? 

39.  12  +  8  +  6  +  4  are  how  many  ? 

40.  24  +  10  +  6  +  12  are  how  many  ? 

41.  22  +  32  +  6  — 10  are  how  many? 

42.  37  +  23  +  15  are  how  many  ? 

43.  64  +  26  +  12  —  8  are  how  many  ? 


ADDITION. 


15 


LESSON  V. 

1.  Three  hoys,  James,  Joseph,  and  Jacob  gave  some 
money  to  a  beggar;  James  gave  him  6,  Joseph  8,  and 
Jacob  10  cents  ;  how  many  cents  did  they  give  him  ? 

2.  Gave  8  cents  to  John,  4  cents  to  Morgan,  and  2 
cents  to  Samuel ;  how  many  cents  did  all  receive  ? 

3.  Henry  has  3  marbles,  Harvey  has  10,  and  Harry 
has  7 ;  how  many  marbles  have  all  ? 

4.  Gave  7  nuts  to  one  boy,  6  to  another,  and  7  to 
another ;  how  many  nuts  did  the  three  boys  receive  ? 

5.  Bought  a  basket  of  strawberries  for  7  cents,  a 
basket  of  cherries  for  4  cents,  and  a  basket  of  plums 
for  8  cents ;  how  many  cents  did  all  cost  ? 

6.  Lydia  has  9  pinks,  Mary  10,  and  Ann  7  ;  how 
many  pinks  have  they  all  ? 

7.  Bought  a  knife  for  14  cents,  and  a  ball  for  12 
cents ;  how  much  did  both  cost  ? 

8.  Gave  18  cents  for  an  arithmetic,  2  for  a  pencil, 
and  10  for  a  slate;  how  much  did  all  cost? 

9.  James  had  12  cents,  and  his  mother  gave  him 
13  more  ;  how  many  had  he  then  ? 

10.  Robert  shot  9  birds,  Richard  shot  11,  and  James 
shot  12  ;  how  many  did  they  shoot  ? 

11.  A  boy  bought  a  pound  of  butter  for  14  ceftts,  a 
pound  of  meat  for  8  cents,  and  a  bunch  of  lettuce  for 
7  cents ;  how  many  cents  did  these  articles  cost  ? 

12.  Bought  a  pound  of  raisins  for  10  cents,  a  pound 
of  candies  for  12  cents,  and  a  pound  of  cinnamon  for 
15  cents ;  how  much  was  the  whole  cost? 

13.  John  had  20  marbles,  Matthew  9,  and  Morgan 
12  ;  how  many  had  they  in  all  ? 

14.  James  bought  a  pigeon  for  9  cents,  a  robin  for 
10  cents,  and  a  squirrel  for  12  cents;  how  much  did 
all  cost  him  ? 

15.  A  lady  bought  some  pins  for  15  cents,  some 


16 


ADDITION, 


thread  for  10  cents,  and  some  lace  for  18  cents;  how 
many  cents  did  all  these  articles  cost  her  ? 

16.  A  gentleman  bought  a  hat  for  6  dollars,  a  vest 
for  5  dollars,  and  a  coat  for  20  dollars;  how  many 
dollars  did  he  pay  for  them  all  ? 

17.  A  man  bought  a  watch  for  40  dollars,  a  gold 
chain  for  15  dollars,  and  a  gold  pen  for  5  dollars ; 
how  much  did  he  pay  for  these  three  articles? 

18.  Jackson  gave  25  cents  to  his  sister,  and  23  to 
his  mother  ;  how  many  cents  did  he  give  away  ? 

19.  Bought  a  barrel  of  flour  for  7  dollars,  a  barrel 
of  pork  for  12  dollars,  and  a  barrel  of  fish  for  11  dol¬ 
lars  ;  how  much  was  the  whole  cost  ? 

20.  Bought  a  horse  for  60  dollars,  a  cow  for  20 
dollars,  and  a  colt  for  25  dollars  ;  how  much  did  all  cost  ? 

21.  If  your  father  should  give  you  12  cents,  your 
mother  14  cents,  and  your  sister  4  cents;  how  many 
cents  would  you  then  have  ? 

22.  A  boy  spent  11  cents  for  confectionery,  9  cents 
for  a  ball,  and  5  cents  for  a  top  ;  how  many  cents  did 
he  spend  for  all  ? 

23.  A  man  bought  some  butter  for  57  dollars,  and 
some  molasses  for  23  dollars  ;  how  many  dollars  did 
both  cost  ? 

24.  A  boy  traveled  17  miles  one  day,  and  23  the 
next  y  how  far  did  he  travel  in  the  two  days  ? 

25.  A  lady  bought  a  hat  for  7  dollars,  a  dress  for 
9  dollars,  and  a  gold  watch  for  60  dollars ;  how  many 
dollars  did  all  cost? 

26.  A  mechanic  sold  a  wagon  for  57  dollars,  and  a 
sleigh  for  43  dollars  ;  how  much  did  he  receive  for 
both  ? 

27.  A  boy  saw  24  pigeons  on  one  tree,  and  36  on 
another;  how  many  did  he  see  in  all? 

28.  In  a  certain  recitation  21  questions  were  an¬ 
swered  correctly,  and  9  incorrectly  ;  how  many  ques¬ 
tions  were  asked  during  the  recitation  ? 


ADDITION. 


17 


29.  Gave  87  dollars  for  a  cliaise,  2  dollars  for  a  whip, 
and  1 1  dollars  for  a  buffalo  robe  ;  how  much  was  given 
for  all  ? 

30.  If  a  horse  is  worth  60  dollars,  and  a  sleigh  75 
dollars,  what  is  the  value  of  both  ? 

31.  Matthew  is  15  years  old,  Morgan  is  7,  and 
Martin  is  10  ;  what  is  the  sum  of  their  ages  ? 

32.  A  man  bought  a  load  of  hay  for  7  dollars,  a 
load  of  rye  for  36  dollars,  and  a  load  of  wheat  for  57 
dollars  ;  how  much  was  the  whole  cost  ? 

33.  A  man  is  48  years  old,  and  his  wife  is  32  years 
old ;  what  is  the  sum  of  their  ages? 

34.  A  farmer  bought  a  horse  for  60  dollars,  and  a 
yoke  of  oxen  for  75  dollars;  how  much  did  the  horse 
and  oxen  together  cost  him  ? 

35.  John  gave  11  candies  to  his  brother,  9  to  his 
sister,  and  kept  12  himself;  how  many  candies  had  he 
at  first  ? 

36.  Simeon  hoed  12  rows  of  corn,  Simon  15,  James 
13,  and  John  11  ;  how  many  rows  did  they  together 
hoe? 

37.  A  merchant  sold  30  barrels  of  flour  one  week, 
37  the  next  week,  and  33  the  following  week  ;  how 
many  barrels  did  he  sell  during  the  three  weeks  ? 

38.  A  merchant  sold  a  barrel  of  sugar  for  5  dollars, 
a  barrel  of  rum  for  15  dollars,  and  a  hogshead  of  mo¬ 
lasses  for  23  dollars ;  how  much  did  he  receive  for  all 
these  articles  ? 

39.  A  man  bought  a  firkin  of  butter  for  9  dollars, 
a  keg  of  molasses  for  7  dollars,  a  box  of  cheese  for  4 
dollars,  and  a  box  of  raisins  for  5  dollars  ;  how  much 
was  the  entire  cost  ? 

40.  A  lady  bought  a  silk  dress  for  18  dollars,  a  muff 
for  12  dollars,  a  shawl  for  17  dollars,  and  a  pair  of 
gloves  for  1  dollar ;  the  entire  cost  is  required. 

2* 


18 


SUBTRACTION. 


CHAPTER  II. 


LESSON  I. 

1.  If  I  have  3  apples,  and  give  1  of  them  to  Rich¬ 
ard,  how  many  shall  I  have  left  ? 

Solution. — If  I  have  3  apples  and  give  1  to  Richard,  I  will 
have  remaining  the  difference  between  3  and  1  which  is  2  apples. 

2.  William  had  4  chestnuts,  and  gave  1  to  his  broth¬ 
er  ;  how  many  had  he  left  ? 

3.  Martha  had  5  books,  and  on  her  way  to  school, 
lost  one  of  them  ;  how  many  had  she  left  ? 

4.  Cornelia  had  6  apples  and  gave  1  to  her  brother  ; 
how  many  had  she  left  ? 

5.  Rachel  had  10  pins  and  lost  1  of  them;  how 
many  had  she  left  ? 

6.  Martha  had  12  pears  and  give  2  to  Elizabeth  ; 
how  many  had  she  left  ? 

7.  If  you  had  5  candies  and  should  give  2  of  them 
away,  how  many  would  you  have  left  ? 

8.  James  had  6  apples  and  gave  2  away  ;  how  many 
had  he  remaining? 

9.  Cornelia  says  she  learned  12  letters  yesterday 
and  has  forgotten  3  of  them ;  how  many  does  she  re¬ 
member  ? 

10.  James  had  10  marbles  and  lost  3;  how  many 
had  he  left  ? 

11.  Mary  found  9  roses  on  her  bush,  and  picked  off 
4  of  them  ;  how  many  remained  on  the  bush  ? 


12. 

13. 

14. 

15. 

16. 


How 

How 

How 

How 

How 


many 

many 

many 

many 

many 


are 

are 

are 

are 

are 


4 

5 
7 
9 
9 


less 

less 

less 

less 

less 


2? 

3? 

3? 

4? 

3? 


: 


SUBTRACTI ON. 


19 


/ 


17.  How  many 

18.  How  many 

19.  How  many 

20.  How  many 

21.  How  many 

22.  How  many 

23.  How  many 

24.  How  many 

25.  How  many 

26.  How  many 

27-  How  many 

28.  How  many 

29.  How  many 

30.  How  many 


are 

9 

less 

7? 

are 

9 

less 

5? 

are 

11 

less 

4? 

are 

10 

less 

4? 

are 

11 

less 

5? 

are 

14 

less 

4? 

are 

8 

less 

5? 

are 

13 

less 

3? 

are 

14 

less 

5? 

are 

17 

less 

7? 

are 

15 

less 

5? 

are 

13 

less 

10  ? 

are 

23 

less 

3? 

are 

27 

less 

7? 

Remark. — The  symbol  — ,  is  called  minus  ;  and  denotes  that 
the  quantity  on  the  right  of  it  is  to  be  taken  from  the  quantity 
on  the  left.  Thus,  6  —  4  —  2  shows  that  4  is  to  be  subtracted 
from  6  ; — and  is  read,  6  minus  4  equal  2. 


31. 

8  — 

5 

are 

how 

many  ? 

32. 

9  — 

7 

are 

how 

many  ? 

33. 

lO- 

8 

are 

how 

many  ? 

34. 

ll— 

8 

are 

1)0  w 

many  ? 

35. 

12- 

6 

are 

how 

many  ? 

36. 

13  — 

•8 

are 

how 

many  ? 

37. 

14  — 

8 

are 

how 

many  ? 

38. 

18  — 

8 

are 

how 

many  ? 

39. 

22  — 

12 

arc 

how 

many  ? 

40. 

24- 

14 

are 

how 

many? 

41. 

12  — 

4 

are 

how 

many  ? 

42. 

28- 

8 

are 

how 

many  ? 

43. 

20  — 

5 

are 

how 

many  ? 

44. 

20- 

8 

are 

how 

many  ? 

45. 

20  — 

9 

are 

how 

many  ? 

46. 

20- 

7 

are 

how 

many  ? 

47. 

20  — 

10 

are 

how 

many  ? 

48. 

20  — 

15 

are 

how 

many  ? 

49, 

24- 

10 

are 

how 

many  ? 

20 

SUBTE 

ACT 

ION. 

50, 

25  —  10  +  5 

are 

how 

51. 

26  —  10  +  4 

are 

how 

52. 

28-10  +  2 

are 

how 

53. 

27-10  +  5 

are 

how 

54. 

29  —  10  +  6 

are 

how 

55. 

32-10  +  8 

are 

how 

56. 

34-10  +  7 

are 

how 

57. 

36  —  10  +  8 

are 

how 

58. 

35  —  10  +  4 

are 

how 

59. 

37  —  10  +  7 

are 

how 

60. 

38  —  10  +  8 

are 

how 

61. 

39  —  10  +  9 

are 

how 

62. 

47  —  10  +  6 

are 

how 

63. 

40  —  12  +  9 

are 

how 

64. 

42  —  20  +  7 

are 

how 

65. 

45  —  20  +  5 

are 

how 

66. 

46  —  20  +  6 

are 

how 

67. 

47  —  20  +  8 

are 

how 

68. 

47-37  +  4 

are 

how 

69. 

49  —  19  +  9 

are 

how 

70. 

71. 

52  —  22  +  10 

lire 

how 

54-34  +  11 

are 

how 

72. 

56  —  46  +  12 

are 

how 

73. 

57-27  +  14 

are 

how 

74. 

58  —  48  +  9 

are 

how 

75. 

62  —  30  +  10 

are 

how 

76. 

65  —  40  +  15 

are 

how 

77. 

68  —  48  +  16 

are 

how 

78. 

74  —  34  +  15 

are 

how 

79.  Gave 

7  cents  for  a  s 

.pool  of  thr< 

many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  tJ 
many  ? 
many  ? 
many  ? 
many  ? 
many? 
many  ? 


the  lemon  ? 

80.  Paid  18  cents  for  a  pound  of  butter,  and  8  cents 
for  a  pound  of  meat ;  how  much  more  was  paid  for  the 
butter  than  for  the  meat  ? 

81.  James  bought  18  candies,  and  gave  John  7  of 
them  ;  how  many  had  he  left  ? 


SUBTRACTION. 


21 


82.  Sold  a  quantity  of  wool  for  27  dollars,  and  re¬ 
ceived  in  payment  a  barrel  of  flour  worth  5  dollars ; 
how  many  dollars  remain  due? 

83.  James  has  27  marbles,  and  John  has  17  ;  how 
many  more  has  James  than  John? 

84.  Harry  is  15  years  old,  and  Ilenry  is  9  years 
old ;  how  many  years  older  is  Harry  than  Henry  ? 

85.  A  teacher  being  ashed  how  many  pupils  he  had, 
answered  that  he  usually  had  37  but  at  present  he  had 
only  27  ;  how  many  were  absent? 

86.  A  man  purchased  a  watch  for  37  dollars,  but 
found  he  had  only  24  dollars  with  him ;  how  much 
must  he  borrow  to  pay  the  balance  ? 

87.  Mr.  A  has  94  sheep,  and  B  has  44  ;  how  many 
more  sheep  has  A  than  B  ? 

88.  Morgan  gave  23  cents  for  some  cake,  and  14 
cents  for  some  cinnamon ;  how  much  more  did  the 
cake  cost  than  the  cinnamon  ? 

89.  Michael  had  29  cents  and  lost  14  ;  how  many 
had  he  left  ? 

90.  In  a  certain  recitation  47  questions  were  asked, 
and  9  of  them  were  answered  incorrectly  ;  how  many 
were  correctly  answered  ? 

91.  A  man  sold  23  sheep  from  a  flock  consisting  of 
93  ;  how  many  sheep  remained? 

92.  Mr.  B  bought  a  horse  for  35  dollars,  and  sold  it 
for  46  dollars  ;  how  much  did  he  gain  ? 

93.  A  cow  was  bought  for  25  dollars  and  sold  for 
19  dollars;  how  much  was  the  loss? 

94.  A  merchant  bought  a  quantity  of  goods  for  95 
dollars,  but  being  damaged  was  obliged  to  sell  them 
for  80  dollars  ;  how  much  did  he  lose?  /  •  ** 

95.  From  a  vessel  containing  57  gallons,  27  gallons 
leaked  out ;  how  much  remained  in  it  ? 

96.  A  merchant  bought  a  quantity  of  silk  for  47 
dollars,  and  sold  it  for  67  dollars ;  how  much  did  he 
gain  by  the  bargain. 

■V  (r 


22  ADDITION  AND  SUBTRACTION. 


97.  A  butcher  has  57  sheep,  and  44  lambs ;  how 
many  more  sheep  has  he  than  lambs? 

98.  Paid  97  dollars  for  a  quantity  of  sugar,  and  43 

dollars  for  some  molasses ;  how  much  more  did  the 
sugar  cost  than  the  molasses  ?  *  . 

- 4  ♦♦ » - 


LESSON  II. 

CHAPTER  FIRST  COMBINED  WITH  THE  PRECEDING  LESSON. 

1.  A  boy  has  7  chestnuts  in  one  hand,  and  4  in  the 
other;  how  many  more  has  he  in  one  hand  than  in 
the  other ;  and  how  many  in  both  ? 

2.  Bought  a  barrel  of  fish  for  8  dollars,  and  some 
quinces  for  3  dollars ;  how  much  more  did  the  fish 
cost  than  the  quinces  ?  What  was  the  cost  of  both  ? 

3.  Gave  15  dollars  for  a  cow  and  6  dollars  for  a 
sheep ;  how  much  more  was  given  for  the  cow  than 
for  the  sheep  ?  How  much  was  given  for  both  ? 

4.  Phineas  gave  50  cents  for  a  grammar,  and  25 
cents  for  an  arithmetic  ;  how  much  was  the  cost  of 
both  ?  How  much  did  one  cost  more  than  the  other  ? 

5.  Paid  15  dollars  for  a  barrel  of  rum,  and  6  dollars 
for  a  barrel  of  flour  ;  how  much  was  the  cost  of  both  ; 
and  how  much  more  did  the  rum  cost  than  the  flour  ? 

6.  Sold  a  firkin  of  butter  for  10  dollars,  a  keg  of 
cheese  for  5  dollars,  and  received  in  payment  a  barrel 
of  flour  worth  6  dollars  ;  how  much  remains  due  ? 

7.  James  gave  12  cents  for  oranges,  15  cents  for 

cake,  and  had  13  cents  remaining ;  how  much  had  he 
at  first  ?  '  / 

8.  Mary  bought  a  comb  for  10  cents,  a  spool  of 
thread  for  12  cents,  and  a  paper  of  needles  for  8  cents  ; 
— she  handed  the  clerk  37  cents;  how  much  change 
ought  she  to  receive  ? 


ADDITION  AND  SUBTRACTION.  23 


9.  A' man  sold  a  cow  for  20  dollars,  a  calf  for  4 
dollars,  and  a  sheep  for  3  dollars  ;  and  in  payment  re¬ 
ceived  a  wasron  worth  17  dollars  ; — how  much  remains 
due? 

10.  A  lady  bought  a  ribbon  for  24  cents,  some  tape 
for  8  cents,  and  some  thread  for  12  cents, — she  had  only 
60  cents  ;  how  much  remained  after  she  paid  for  these 
articles?  / * 

11.  Stephen,  at  a  game  of  marbles,  won  4  and  lost 
6,  and  then  had  only  8  remaining;  how  many  had  he 
at  first  ? 

12.  Sampson  having  9  apples,  gave  4  to  his  mother, 
and  3  to  his  sister  ; — for  his  generosity  his  father  gave 
him  13  more;  how  many  had  he  then?  * 

13.  A  man  bought  some  cloth  for  12  dollars,  and 
sold  it  for  18  dollars  ;  how  much  was  his  gain  ? 

14.  A  farmer  bought  a  horse  for  63  dollars,  and 
exchanged  it  for  a  yoke  of  oxen, — these  lie  sold  for  87 
dollars  ;  how  much  did  he  gain  by  the  operation  ? 

15.  A  man  bought  a  yoke  of  oxen  for  97  dollars, 
their  services  amounted  to  40  dollars,  and  their  keep¬ 
ing  to  13  dollars, — he  then  sold  them  for  80  dollars  ; 
did  he  gain  or  lose,  and  how  much  ? 

16.  A  box  of  raisins  was  bought  for  3  dollars,  a 
firkin  of  butter  for  15  dollars,  and  were  both  sold  for 
20  dollars  ;  how  much  was  gained  ? 

17.  A  farmer  sold  a  cow  for  29  dollars,  which  was 
5  dollars  more  than  she  cost ;  how  much  did  she  cost  ? 

18.  A  drover  bought  some  sheep  for  40  dollars,  some 
cattle  for  130  dollars,  and  sold  them  all  for  200  dol¬ 
lars  ;  how  much  was  his  gain  ? 

19.  A  jeweler  bought  a  watch  for  20  dollars,  a 
chain  for  10  dollars,  a  key  for  2  dollars,  and  sold  them 
all  for  42  dollars ;  how  much  did  he  gain  by  the  bar¬ 
gain  ? 

20.  24  +  12  +  9  are  how  many  ? 

21.  10  +  30  +  15  are  how  many  ? 


24  ADDITION  AND  SUBTEACTION. 

22.  14  + 16  + 11  are  how  many  ? 

23.  36  +  9  — 12  are  how  many  ? 

24.  38  +  22  — 15  are  how  many  ? 

25.  43  +  37  —  20  are  how  many? 

26.  13  +  26  —  25  are  how  many  ? 

27.  44  —  22  +  10  — 12  are  how  many? 

28.  27  +  23  —  20  +  2  are  how  many? 

29.  15  +  25  —  30  +  15  are  how  many?  ) 

30.  20  +  40  —  30  +  10  are  how  many? 

31.  A  boy  bought  a  ball  for  6  cents ;  for  how  much 
must  he  sell  it  to  gain  4  cents  ? 

32.  A  merchant  bought  a  hogshead  of  molasses  for 
47  dollars,  and  paid  3  dollars  for  cartage  ;  for  how 
much  must  he  sell  it  to  gain  1 2  dollars  ? 

33.  A  grocer  bought  a  hogshead  of  sugar  for 
30  dollars;  for  what  must  he  sell  it  to  gain  18  dol¬ 
lars  ? 

34.  A  drover  bought  sheep  as  follows :  of  one  man 
he  bought  24,  of  another  8,  and  of  another  22  :  he 
then  sold  20  of  them  ;  how  many  remained  unsold  ? 

35.  A  watch  cost  40  dollars  ;  how  must  it  be  sold 
to  gain  13  dollars  ? 

36.  Four  boys  bought  a  mellon  ;  one  gave  3  cents, 
another  4,  another  8,  and  the  other  6;  how  much  did 
they  pay  for  the  melon? 

37.  Mary  bought  16  candies  at  one  shop,  and  13  at 
another, — on  her  way  home  she  ate  11  of  them;  how 
many  had  she  left  ? 

38.  Matthew  had  9  nuts,  Mary  gave  him  10  more, 
and  John  gave  him  enough  to  make  his  number  39  ; 
how  many  did  John  give  him  ? 

39.  A  farmer  had  25  sheep  in  one  field  and  15  in 
another, — he  then  bought  enough  more  to  make  his 
number  56  ;  how  many  did  he  buy  ? 

40.  John  has  34  marbles,  and  Albert  25  ;  how  many 
have  they  both  ;  and  how  many  more  has  John  than 
Albert  ? 


MULTIPLICATION. 


25 


CHAPTER  III. 


LESSON  I. 

1. 

Two 

times 

1 

are 

how 

many  ? 

2. 

Two 

times 

2 

are 

how 

many  ? 

3. 

Two 

times 

3 

are 

how 

many  ? 

4. 

Two 

times 

4 

are 

how 

many  ? 

5. 

Two 

times 

5 

are 

how 

many  ? 

6. 

Two 

times 

6 

are 

how 

many  ? 

7. 

Two 

times 

7 

are 

how 

many  ? 

8. 

Two 

times 

8 

are 

how 

many  ? 

9. 

Two 

times 

9 

are 

how 

many  ? 

10. 

Two 

times 

10 

are 

how 

many  ? 

11. 

Two 

times 

11 

are 

how 

many  ? 

12. 

Two 

times 

12 

are 

how 

many  ? 

13.  What  will  2  oranges  cost,  at  3  cents  a  piece? 

Solution. — If  1  orange  cost  3  cents,  2  oranges  will  cost  two 
times  3  cents ;  which  are  6  cents. 

14.  What  will  2  peaches  cost,  at  2  cents  a  piece  ? 

15.  What  will  2  apples  cost,  at  3  cents  a  piece? 

16.  What  will  2  pine-apples  cost,  at  8  cents  a  piece  ? 

17.  What  will  2  pounds  of  meat  cost,  at  5  cents  a 
pound  ? 

1 8.  What  will  2  pounds  of  cinnamon  cost,  at  1 1  cents 
a  pound? 

19.  What  will  2  pounds  of  raisins  cost,  at  12  cents 
a  pound  ? 

20.  What  will  2  citrons  cost,  at  10  cents  a  piece? 

21.  What  will  2  quarts  of  cherries  cost,  at  9  cents 
a  quart  ? 

22.  What  will  2  lemons  cost,  at  4  cents  a  piece? 

23.  Three  times  2  are  how  many  ? 

24.  Three  times  3  are  how  many? 

25.  Three  times  4  are  how  many  ? 

3 


26 


MULTIPLICATION. 


26.  Three 

times 

5 

are 

how 

many? 

27.  Three 

times 

6 

are 

how 

many  ? 

28.  Three 

times 

7 

are 

how 

many  ? 

29.  Three 

times 

8 

are 

how 

many  ? 

30.  Three 

times 

9 

are 

how 

many  ? 

31.  Three 

times 

10 

are 

how 

many  ? 

32.  Three 

times 

11 

are 

how 

masy  ? 

33.  Three 

times 

12 

are 

how 

many  ? 

J 

34.  Four 

times 

3 

are 

how 

many? 

35.  Four 

times 

4 

are 

how 

many  ? 

36.  Four 

times 

5 

are 

how 

many  ? 

37.  Four 

times 

6 

are 

how 

many  ? 

38.  Four 

times 

7 

arc 

how 

many  ? 

39.  Four 

times 

8 

are 

how 

many  ? 

40.  Four 

times 

9 

are 

how 

many  ? 

41.  Four 

times 

10 

are 

how 

many  ? 

42.  Four 

times 

11 

are 

how 

many  ? 

43.  Four 

times 

12 

are 

how 

many  ? 

44.  What  will  3  quarts  of  cherries  cost,  at  6  cents  a 
quart  ? 

45.  What  will  3  lead  pencils  cost,  at  5  cents  a  piece  ? 

46.  What  will  3  quarts  of  milk  cost,  at  4  cents  a 
quart  ? 

47.  What  will  3  yards  of  ribbon  cost,  at  7  cents  a  yd.? 

48.  What  will  4  quarts  of  chestnuts  cost,  at  6  cents 
a  quart  ? 

49.  What  will  4  yards  of  edging  cost,  at  5  cents  a 
yard  ? 

50.  What  will  3  ounces  of  snuff  cost,  at  8  cents  an 
ounce  ? 

51.  What  will  4  ounces  of  cinnamon  cost,  at  7  cents 
an  ounce? 

52.  What  will  3  pounds  of  cheese  cost,  at  10  cents 
a  pound  ? 

53.  What  will  4  sheets  of  wadding  cost,  at  8  cents 
a  sheet? 

54.  What  will  3  yards  of  calico  cost,  at  11  cents  a 
yard  ? 


MULTIPLICATION. 


27 


55.  What  will  4  skeins  of  silk  cost,  at  9  cts.  a  skein? 

56.  What  will  3  yards  of  ribbon  cost,  at  12  cents  a 
yard  ? 

57.  What  will  4  pounds  of  starch  cost,  at  12  cents 
a  pound  ? 

58.  What  will  4  candlesticks  cost,  at  1  lets,  a  piece  ? 

59.  What  will  4  tops  cost,  at  10  cents  a  piece  ? 

60.  What  will  5  apples  cost,  at  4  cents  a  piece  ? 


61. 

Five 

times 

6 

are 

how 

many  ? 

62. 

Five 

times 

7 

are 

how 

many  ? 

63. 

Five 

times 

9 

are- 

how 

many  ? 

64. 

Five 

times 

8 

are 

how 

many  ? 

65. 

Five 

times 

5 

are 

how 

many  ? 

66. 

Five 

times 

10 

are 

how 

many  ? 

67. 

Five 

times 

12 

are 

how 

many  ? 

68. 

Five 

times 

11 

are 

how 

many? 

69. 

Six 

times 

6 

are 

how 

many  ? 

70. 

Six 

times 

8 

are 

how 

many  ? 

71. 

Six 

times 

7 

are 

how 

many  ? 

72. 

Six 

times 

10 

are 

how 

many  ? 

73. 

Six 

times 

9 

are 

how 

many  ? 

74. 

Six 

times 

12 

are 

how 

many  ? 

75. 

Six 

times 

11 

are 

how 

many  ? 

76.  Seven  times  6  are  how  many  ? 

77.  Seven  times  8  are  how  many? 

78.  Seven  times  7  are  how  many? 

79.  Seven  times  10  are  how  many? 

80.  Seven  *  times  9  are  how  many? 

81.  Seven  times  12  are  how  many? 

82.  Seven  times  11  are  how  many? 

83.  What  will  5  barrels  of  flour  cost,  at  6  dollars  a 
barrel  ? 

84.  What  will  5  bushels  of  potatoes  cost,  at  5  dimes 
a  bushel  ? 

85.  What  will  6  primers  cost,  at  6  cents  a  piece? 

86.  What  will  5  barrels  of  fish  cost,  at  7  dollars  a 
barrel  ? 


28 


MULTIPLICATION. 


87.  What  will  6  pounds  of  mutton  cost,  at  7  cents 
a  pound  ? 

88.  What  will  5  barrels  of  sugar  cost,  at  12  dollars 
a  barrel  ? 

89.  What  will  6  pounds  of  sturgeon  cost,  at  10  cents 
a  pound  ? 

90.  What  will  6  pounds  of  almonds  cost,  at  12  cents 
a  pound  ? 

91.  What  will  5  barrels  of  pork  cost,  at  $10  a  bbl.  ? 

92.  What  will  6  pounds  of  candles  cost,  at  9c.  a  lb.  ? 

93.  What  will  5  coats  cost,  at  9  dollars  a  piece  ? 

94.  What  will  6  handkerchiefs  cost,  at  11  cents  a 
piece  ? 

95.  What  will  6  inkstands  cost,  at  8  cents  a  piece? 

96.  What  will  7  lamps  cost,  at  9  dimes  a  piece  ? 

97.  What  will  7  plows  cost,  at  8  dollars  a  piece  ? 

98.  What  will  7  boxes  of  caps  cost,  at  10c.  a  box? 

99..  What  will  7  quires  of  paper  cost,  at  12  cents  a 

quire  ? 

100.  What  will  7  letter-folders  cost,  at  11  cents  a 
piece  ? 

101.  Eight 

102.  Eight 

103.  Nine 

104.  Eight 

105.  Nine 

106.  Eight 

107.  Nine 

108.  Eight 

109.  Nine 

110.  Eight 

111.  Nine 

112.  What  will  9  bunches  of  roses  cost,  at  9  cents  a 
bunch  ? 

113.  What  will  8  pen-knives  cost,  at  12  cts.  a  piece? 

114.  What  will  9  bunches  of  grapes  cost,  at  12  cents 
a  bunch  ? 


times 

8 

are 

how 

many  ? 

times 

10 

are 

how 

many  ? 

times 

8 

are 

how 

many  ? 

times 

7 

are 

how 

many  ? 

times 

9 

are 

how 

many  ? 

times 

9 

are 

how 

many  ? 

times 

11 

are 

how 

many  ? 

times 

12 

are 

how 

many  ? 

times 

10 

are 

how 

many  ? 

times 

11 

are 

how 

many  ? 

times 

12 

are 

how 

many  ? 

- 

mu 

HUH 

jj ,«  f  :.S  y  . ' 

• :  J  a  ij. 

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.  . 

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'  i  *  > » • 

\  i  V  *  *• 

Mo. 

HU;,' 

'  \  ‘  *  '  •  *;  »  1  A  V  *  •  <’  ■  l  .  k  >  •• 

V  ,\M  '•  -  : 

■ 1  V  I,1'*'  :  •  >■ 

VvS.iK' 

'  .  V'  ’  \  '  . 

■  M 

■  •  'v::l 

MULTIPLICATION.  29 

115.  What  will  11  yards  of  calico  cost,  at  11  cents 
a  yard  ? 

116.  What  will  10  halls  of  cotton  cost,  at  12  cents 
a  ball  ? 

11 7.  What  will  11  pounds  of  ginger  cost,  at  12  cents 
a  pound  ? 

118.  What  will  10  blocks  of  tape  cost,  at  8  cents  a 
block  ? 

119.  What  will  12  yards  of  cloth  cost,  at  12  dimes 
a  yard  ? 

120.  What  will  13  pair  of  boots  cost,  at  $4  a  pair? 


LESSON  II. 

CHAPTERS  FIRST  AND  SECOND  COMBINED  WITH  THE  PRECEDING  LESSON. 

1.  At  7  cents  a  piece,  what  will  9  pine-apples  cost? 

2.  If  the  postage  on  1  letter  is  3  cents,  what  will  be 
the  postage  on  8  letters  ? 

3.  If  it  require  8  yards  of  calico  to  make  1  dress, 
how  many  yards  will  it  require  to  make  7  dresses  ? 

4.  If  John  obtain  2  credit-marks  in  1  day,  how  many 
will  he  have  in  15  days  ? 

5.  A  man  hired  a  horse  to  ride  12  miles,  at  the  rate 
of  5  cents  a  mile ;  how  much  must  he  pay  ? 

6.  Margaret’s  cloak  contains  7  yards  of  merino, 
worth  9  dimes  a  yard  ;  what  is  the  value  of  her  cloak  ? 

7.  If  a  stage-coach  go  9  miles  in  an  hour,  how  far 
will  it  go  in  7  hours  ? 

8.  At  2  dollars  a  week,  how  much  will  20  weeks’ 
board  amount  to  ? 

9.  The  fare  by  railroad  from  Albany  to  Boston  is 
5  dollars  for  1  person  ;  how  much  will  it  be  for  a 
family  of  9  persons  ? 


3* 


30 


MULTIPLICATION. 


10.  Helen  liad  8  rose  bushes,  and  there  were  7  roses 
on  each  ;  how  many  roses  had  she  in  all  ? 

11.  At  3  dimes  a  gallon,  what  will  15  gallons  of 
molasses  cost? 

12.  There  are  10  rows  of  trees  in  an  orchard,  and 
12  trees  in  each  row;  how  many  trees  are  there  in  the 
orchard  ? 

13.  A  traveler  meeting  13  beggars,  gave  to  each  of 
them  3  dimes ;  how  many  dimes  did  he  give  to  all  of 
them  ? 

14.  A  woman  bought  11  yards  of  cloth  and  paid  for 
it  with  butter, — giving  9  pounds,  for  a  yard  ;  how  many 
pounds  of  butter  did  it  take'  to  pay  for  the  cloth  ?  How 
much  did  the  cloth  cost  provided  the  butter  was- worth 
10  cents  a  pound  ? 

15.  In  a  certain  corn  field  there  are  24  rows,  and 
30  hills  in  each  row  ;  how  many  hills  in  the  field  ? 

16.  What  will  40  steel  pens  cost,  at  2  cents  a 
piece  ? 

17.  What  will  8  pair  of  snuffers  cost,  at  3  dimes  a 
pair  ? 

18.  When  2  dimes  are  paid  for  1  duck,  what  will  be 
the  cost  of  8  ducks  ?  of  10  ducks  ?  of  12  ducks  ? 

19.  When  hay  is  worth  8  dollars  a  ton,  what  is  the 
value  of  2  tons  ?  of  4  tons  ?  of  3  tons  ?  of  7  tons  ?  of 
5  tons  ?  of  10  tons  ?  of  12  tons  ?  of  14  tons? 

20.  At  2  dimes  a  piece,  how  many  cents  will  4  books 
cost?  6  books?  10  books?  12  books?  11  books?  7 
books?  16  books?  13  books?  14  books? 

21.  If  5  cents  will  buy  1  primer,  what  will  be  the 
cost  of  4  primers  ?  of  6  ?  of  9  ?  of  8  ?  of  10  ? 

22.  6  plates,  at  5  dimes  a  piece,  will  cost  how 
much  ? 

23.  At  5  dimes  a  piece,  how  much  will  4  handker¬ 
chiefs  cost  ?  6?  8?  10?  12?  14?  11?  16? 

24.  At  6  dimes  a  piece,  how  many  cents  will  2  geese 
cost?  4?  5?  8?  10?  12?  9?  7? 


MULTIPLICATION. 


31 


25.  At  12  cents  a  piece,  how  much  will  3  candle¬ 
sticks  cost  ?  How  much  will  6?  5  ?  8?  9?  10?  7? 

26.  If  I  pay  5  cents  for  riding  1  mile,  how  much 
must  I  pay  for  riding  7  miles?  8  miles?  9?  6  ?  10  ?  12  ? 

27.  At  7  cents  a  yard,  how  much  will  5  yards  of 
ribbon  cost  ?  6  yards  ?  8  yards?  9  yards?  10  yards? 
1 2  yards  ? 

28.  If  a  tooth-brush  cost  18  cents,  how  much  will  4 
cost  ? 

29.  9  turkeys  will  cost  how  much,  at  8  dimes  a  piece  ? 

30.  At  14  cents  a  quire,  how  much  will  2  quires  of 
paper  cost  ?  3  quires  ?  4  quires  ?  5  quires  ? 

31.  How  much  will  7  pictures  cost,  at  5  cents  a 
piece?  at  6  cents  a  piece?  at  8  cents  a  piece?  at  10 
cents  a  piece  ? 

32.  How  much  will  8  knives  cost  at  6  dimes  a  piece  ? 
at  10  dimes  a  piece? 

33.  At  10  dimes  a  piece, how  much  will  4  caps  cost* 
5?  6?  8?  9?  12?  14?  17?  19?  21?  25? 

34.  At  40  cents  a  day,  how  much  will  2  day’s  work 
amount  to  ?  5  days  work  ? 

35.  If  one  paper  of  candies  cost  6  cents,  how  much 
will  3  papers  cost?  5  papers?  8  papers?  12  papers? 

36.  At  7  dollars  a  hundred,  how  much  will  4  hun¬ 
dred  feet  of  cedar  boards  cost?  9  hundred  feet?  10 
hundred  feet  ? 

37.  If  1  bushel  of  wheat  cost  60  cents,  how  much 
will  6  bushels  cost?  4  bushels?  5  bushels? 

38.  How  much  will  8  muffs  cost  at  5  dollars  each? 

39.  How  much  will  19  lead  pencils  cost,  at  5  cents 
each  ? 

40.  How  much  will  11  boxes  of  cheese  cost,  at  4 
dollars  a  box  ?  at  5  dollars  a  box  ?  at  8  dollars  a  box  ? 

41.  How  much  will  12  barrels  of  pork  cost  at  5  dol¬ 
lars  a  barrel  ?  at  8  dollars  ?  at  9  dollars  ?  at  10  dollars  ? 

42.  How  much  will  9  tons  of  hay  cost,  at  13  dol¬ 
lars  a  ton  ? 


32 


ADDITION,  SUBTRACTION, 

43.  James  is  9  years  old,  and  liis  father  is  4  times 
as  old  as  he ;  how  old  is  his  father  ? 

44.  Jane’s  frock  contains  7  yards  of  silk,  worth  8 
dimes  a  yard  ;  what  was  the  value  of  the  silk  ?  Pro¬ 
vided  the  making  cost  2  dollars  ;  how  much  was  the 

•  cost  of  her  dress  ? 

45.  If  a  barrel  of  flour  will  serve  12  men  8  days, 
how  long  will  it  serve  1  man  ? 

46.  If  I  earn  12  dollars  in  a  month  and  spend  8, 
how  much  shall  I  have  at  the  end  of  12  months  ? 

47.  If  I  earn  12  dollars  a  month,  and  pay  25  cents 
a  week  for  washing,  and  2  dollars  a  week  for  board, 
how  much  will  I  have  at  the  end  of  40  weeks  (10 
months)  ? 

48.  If  I  buy  9  tons  of  hay,  at  12  dollars  a  ton,  and 
and  sell  6  tons,  at  15  dollars  a  ton,  and  the  3  remain¬ 
ing  tons,  at  10  dollars  a  ton  ;  how  much  shall  I  gain 
by  the  operation  ? 

49.  Bought  11  yards  of  broadcloth,  at  4  dollars 
a  yard,  but,  being  damaged,  I  was  obliged  to  lose 
18  dollars  by  the  sale  of  it ;  how  much  did  I  receive 
for  it  ? 

50.  If  I  buy  12  barrels  of  pork,  at  8  dollars  a  bar¬ 
rel,  and  sell  it  all  for  108  dollars,  how  much  shall  I 
gain  by  so  doing?  J'2 

51.  A  man  bought  a  horse  for  80  dollars,  paid  2 
dollars  a  week  for  his  keeping,  and  received  4  dollars 
a  week  for  his  work  ; — at  the  expiration  of  10  weeks 
he  sold  him  for  70  dollars ;  how  much  did  he  gain  by 
the  operation  ? 

52.  For  how  much  must  I  sell  4  barrels  of  wheat 
which  cost  me  8  dollars  a  barrel,  to  gain  8  dollars? 

53.  What  is  the  cost  of  9  cows,  at  25  dollars 
each  ? 

54.  Provided  a  hunter  should  kill  5  pigeons  and 
wound  4  at  every  shot;  how  many  would  he  kill  and 
wound  respectively,  by  shooting  8  times?  / 


AND  MULTIPLICATION. 


33 


55.  If  a  man  travel  29  miles  in  a  day,  how  many 
miles  will  he  travel  in  6  clays  ? 

56.  How  much  will  8  months’  wages  amount  to,  at 
18  dollars  a  month  ? 

57.  If  10  men  eat  18  pounds  of  butter  in  1  week, 
how  long  would  it  last  1  man  ? 

58.  If  80  dollars  will  pay  for  4  dinners  for  20  men, 
how  many  dinners  would  it  buy  for  1  man  ? 

59.  Bought  3  yards  of  cloth  for  a  coat,  at  7  dollars 
a  yard,  the  buttons  and  cord  cost  2  dollars,  buckram 
and  wadding  1  dollar, — paid  for  making  it  6  dollars ; 
for  how  much  must  I  sell  it  to  gain  5  dollars  ? 

60.  If  17  men  can  do  a  piece  of  work  in  9  days, 
how  many  days  would  it  take  1  man  to  perform  the 
same  work  ? 

61.  Two  men  start  from  the  same  place,  and  travel 
in  opposite  directions ; — one  at  the  rate  of  7  miles  an 
hour,  the  other,  9  miles  an  hour ;  how  far  apart  will 
they  be  in  2  hours  ? 

62.  Two  men  start  from  the  same  place,  and  travel 
the  same  way  ; — one  at  the  rate  of  3  miles  an  hour,  the 
other,  8  miles  an  hour ;  how  far  apart  will  they  be  at 
the  end  of  8  hours  ? 

63.  Two  men  are  50  miles  apart,  and  approach  each 
other4; — one  at  the  rate  of  2  miles  an  hour,  the  other, 
3  miles  an  hour  ;  how  far  apart  will  they  be  at  the  end 
of  5  hours  ? 

64.  If  1  orange  is  worth  4  apples,  how  many  apples 
must  be  given  for  13  oranges  ? 

65.  A  man  earned  80  cents  a  day,  and  paid  50  cents 
a  day  for  his  board  and  washing ;  how  much  had  he 
left  at  the  expiration  of  6  days  ? 

66.  Jane  bought  4  yards  of  silk,  at  2  dollars  a  yard, 

3  shawls,  at  10  dollars  each,  and  some  delaine  for  10 
dollars ;  she  paid  5  ten-dollar  bills  ;  how  much  ought 
she  to  receive  back  ? 

67.  Mary  bought  5  yards  of  silk,  at  8  dimes  a  yard, 


34  ADDITION  —  MULTIPLICATION. 

and  8  yards  of  linen,  at  9  dimes  a  yard  ;  how  many 
yards  did  she  buy,  and  how  much  did  all  cost? 

68.  In  a  certain  school  there  are  12  girls,  and  3 
times  as  many  boys,  less  8 ;  how  many  boys  in  the 
school,  and  how  many  boys  and  girls  together? 

69.  John  has  7  books,  and  Mary  has  4  times  as 
many,  less  18  ;  how  many  has  Mary,  and  how  many 
have  both  ? 

70.  Albert  has  9  marbles,  Aaron  3  times  as  many, 
less  7,  and  Amos  has  twice  as  many  as  both,  less 
8 ;  how  many  has  each,  and  how  many  have  they 
together  ? 

71.  Perry  worked  for  Elisha  4  days,  at  6  dimes  a 
day  ; — Elisha  gave  him  7  bushels  of  corn,  at  3  dimes  a 
bushel ;  how  much  was  then  due  Perry  ? 

72.  A  merchant  bought  25  pounds  of  sugar  for  125 
cents,  and  sold  1 5  pounds  of  it,  at  6  cents  a  pound,  and 
the  remaining  10  pounds,  at  4  cents  a  pound;  how 
much  did  he  gain  by  so  doing  ? 

73.  If  the  interest  on  1  dollar  for  a  year  is  6  cents, 
how  much  is  the  interest  on  13  dollars  for  the  same 
time  ? 

74.  What  will  27  pounds  of  beef  cost,  at  4  cents  a 
pound  ? 

75.  When  beef  is  5  cents  a  pound,  and  pork  9 
cents;  how  much  more  will  9  pounds  of  pork  cost  than 
9  pounds  of  beef? 

76.  Mary  bought  35  quarts  of  milk,  and  on  her  way 
home  she  spilled  4  times  2  quarts,  less  3  quarts  ;  how 
many  quarts  had  she  remaining  ? 

77.  Henry  is  4  feet  in  height  and  John  is  5  ;  and  5 
times  the  sum  of  their  heights,  considered  as  a  num¬ 
ber,  is  equal  to  their  father’s  age  +  15  years.  Re¬ 
quired,  the  father’s  age. 

78.  If  an  orange  cost  2  cents,  a  lemon  twice  as 
much,  and  a  melon  4  times  as  much  as  the  orange  and 


DIVISION. 


35 


lemon  together,  less  14  cents,  how  much  more  will  3 
melons  cost  than  3  oranges  and  3  lemons  ? 

79.  James  has  9  walnuts,  John  twice  as  many 

less  8,  and  Joseph  twice  as  many  as  James  and 
John  +  7  ;  how  many  has  each,  and  how  many  have 
all  ?  0  , 

80.  If  an  apple  cost  2  cents,  an  orange  three  times 
as  much  less  4  cents,  and  a#pine-apple  three  times  as 
much  as  the  apple  and  orange  +  5  cents,  what  will  be 
the  cost  of  all  three  ? 

- ■»♦♦♦«*» - - 


/ 


1. 

Solution. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 
9. 

10. 

11. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 


CHAPTER  IY. 

LESSON  I. 

8  are  how  many  times  2  ? 

8  are  4  times  2,  [because  4  times  2  are  8.] 


6  ■ 

are 

how 

4 

are 

how 

10 

are 

how 

12 

are 

how 

14 

are 

how 

6 

are 

how 

9 

are 

how 

12 

are 

how 

15 

are 

how 

18 

are 

how 

21 

are 

how 

24 

are 

how 

16 

are 

how 

18 

are 

how 

20 

are 

how 

22 

are 

how 

24 

are 

how 

26 

are 

how 

28 

are 

how 

many  times  2  ? 
many  times  2  ? 
many  times  2  ? 
many  times  2  ? 
many  times  2  ? 
many  times  3  ? 
many  times  3  ? 
many  times  3  ? 
many  times  3  ? 
many  times  3  ? 
many  times  3  ? 
many  times  3  ? 
many  times  2  ? 
many  times  2  ? 
many  times  2  ? 
many  times  2  ? 
many  times  2  ? 
many  times  2  ? 
many  times  4  ? 


I' 


36  DIVISION. 

21.  At  2  cents  a  piece,  how  many  apples  can  you 
buy  for  4  cents  ? 

Solution. — If  for  2  cents  I  can  buy  1  apple,  for  4  cents  I  can 
buy  as  many  apples  as  2  is  contained  times  in  4,  which  are  2. 

Remark. — The  following  solution  is  preferred  to  the  above,  if 
the  pupils  are  acquainted  with  Fractions. 

Solution. — If  for  2  cents  I  can  buy  1  apple  for  1  cent  I  can 
buy  i  of  an  apple ;  and  for  4  cents,  4  times  which  are  |,  or  2 
apples. 

22.  At  2  cents  a  piece,  how  many  oranges  can  I  buy 
for  6  cents? 

23.  At  2  cents  a  piece,  how  many  peaches  can  be 
bought  for  8- cents? 

24.  At  3  dimes  a  yard,  how  many  yards  of  calico 
can  be  bought  for  12  dimes? 

25.  At  3  cents  a  piece,  how  many  lemons  can  be 
bought  for  9  cents  ? 

26.  At  2  cents  a  yard,  how  many  yards  of  tape  can 

be  bought  for  10  cents?  % 

27.  At  2  dimes  a  bushel,  how  many  bushels  of 
apples  may  be  had  for  12  dimes? 

28.  How  many  pounds  of  ginger,  at  2  dimes  a 
pound  may  be  had  for  14  dimes? 

29.  How  many  baskets  of  strawberries,  at  3  cents 
a  basket  can  be  had  for  15  cents  ? 

30.  For  16  dollars  ;  how  many  yards  of  cloth  can 
be  had,  at  2  dollars  a  yard  ? 

31.  For  18  apples;  how  many  oranges  can  be  bought 
at  the  rate  of  2  apples  for  1  orange  ? 

32.  How  many  primers,  at  2  cents  a  piece,  can  be 
bought  for  24  cents  ? 

33.  How  many  barrels  of  flour,  at  2  dollars  a  bar¬ 
rel,  can  be  bought  for  20  dollars  ? 

34.  For  22  dollars  ;  how  many  sheep  may  be  bought, 
at  2  dollars  a  piece? 

35.  How  many  melons  may  be  had  for  18  dimes,  at 
3  dimes  a  piece  ? 


T3 

DIVISION.  37 

36.  At  3  cents  a  piece,  how  many  tops  may  be  had 
for  6  cents  ? 

37.  If  1  peck  of  beans  cost  3  dimes,  how  many 
pecks  can  be  bought  for  21  dimes  ? 

38.  At  3  cents  a  mile,  how  many  miles  can  I  ride 
for  24  cents  ? 

39.  How  many  bushels  of  rye,  at  4  dimes  a  bushel, 
may  be  bought  for  12  dimes? 

40.  How  many  books,  at  4  dimes  each,  can  be 
bought  for  20  dimes  ? 

41.  8  are  how  many  times  4  ? 

42.  12  are  how  many  times  4  ? 

43.  16  are  how  many  times  4  ? 

44.  10  are  how  many  times  5  ? 

45.  15  are  how  many  times  5  ? 

46.  20  are  how  many  times  5  ? 

47.  28  are  how  many  times  7  ? 

48.  32  are  how  many  times  4  ? 

49.  30  are  how  many  times  5  ? 

50.  35  are  how  many  times  5  ? 

51.  36  are  how  many  times  4  ? 

52.  40  are  how  many  times  5  ? 

53.  44  are  how  many  times  4  ? 

54.  30  are  how  many  times  '6  ? 

55.  48  contains  8  how  many  times  ? 

Solution. — 48  contains  8,  6  times  [because  6  times  8  are  48.] 

56.  24  contains  8  how  many  times?  4  ?  12  ?  3?, 

57.  36  contains  9  how  many  times?  6?  3?  2? 

58.  54  contains  2  how  many  times  ?  3  ?  9  ? 


59.  75  contains  3  how  many  times?  5  ?  15?  | 

60.  68  contains  2  how  many  times?  4?  1 

61.  At  5  dimes  each,  how  many  turkeys  can  be  had 
for  25  dimes  ? 

62.  If  the  wages  of  1  day  is  4  dimes,  what  will  be 
the  wages  for  9  days  ? 

63.  How  many  days  will  a  man  be  required  to  work 
for  12  dimes,  if  he  receive  4-  dimes  a  day  ? 


38 


DIVISION. 


64.  If  a  boy  spends  5  cents  a  day,  bow  many  days 
will  it  take  him  to  spend  1 5  cents  ? 

65.  A  boy  bad  20  marbles,  and  divided  them 
equally  among  his  5  brothers ;  bow  many  did  each 
receive  ? 

66.  A  boy  divided  28  cents  equally  among  4  poor 
women  ;  bow  many  cents  did  each  receive  ? 

67.  A  farmer  gave  4  of  bis  laborers  32  bushels  of 
corn;  bow  many  bushels  did  each  receive? 

68.  If  5  quarts  of  molasses  cost  30  cents,  wliat  will 
1  quart  cost  ? 

69.  At  5  cents  a  yard,  bow  many  yards  of  ribbon 
may  be  bad  for  35  cents  ?  bow  many  for  50  cents  ? 

70.  IIow  many  pine-apples,  at  8  cents  each,  can  be 
obtained  for  40  cents  ?  for  56  cents  ? 

71.  If  a  man  travel  45  miles  in  9  hours,  bow  many 
miles  does  be  travel  in  1  hour  ? 

72.  If  a  man  travel  5  miles  in  an  hour,  bow  many 
hours  will  it  take  him  to  travel  40  miles  ? 

73.  How  many  yards  of  cloth,  at  4  dollars  a  yard, 
can  you  buy  for  32  dollars  ? 

74.  In  a  certain  orchard  there  are  48  trees  standing 
in.  rows,  and  6  trees  in  each  row  ;  bow  many  rows  are 
there  in  the  orchard  ? 

75.  For  56  dollars,  bow  many  barrels  of  pork  can 
be  bought,  at  8  dollars  a  barrel  ? 

76.  If  a  man  can  travel  6  miles  in  an  hour,  bow 
long  will  it  take  him  to  travel  42  miles  ? 

77.  How  many  yards  of  cloth,  at  4  dollars  a  yard, 
can  you  buy  for  36  dollars  ? 

78.  A  butcher  gave  39  dollars  for  sheep,  at  the  rate 
of  3  dollars  a  head  ;  how  many  sheep  did  he  buy  ? 

79.  45  dollars  were  given  for  9  barrels  of  flour; 
how  much  was  it  a  barrel  ? 

80.  How  long  would  it  take  to  travel  72  miles,  at 
the  rate  of  3  miles  an  hour  ? 


DIVISION. 


39 


LESSON  II. 


1.  20  are  how  many  times  2  ?  4  ?  10  ? 

2.  22  are  how  many  times  11  ? 

3.  24  are  how  many  times  3  ?  4  ?  2  ? 

4.  25  are  how  many  times  5  ? 

5.  28  are  how  many  times  2  ?  7  ? 

6.  30  are  how  many  times  2  ?  3  ?  5  ? ' 

7.  32  are  how  many  times  2?  4?  16?  8? 

8.  34  are  how  many  times  17  ? 

9.  40  are  how  many  times  2?  4  ?  5  ?  8  ? 

10.  44  are  how  many  times  2  ?  11  ? 

11.  46  are  how  many  times  23  ? 

12.  48  are  how  many  times  2?  3?  4?  6? 

13.  50  are  how  many  times  2  ?  10  ? 

14.  56  are  how  many  times  2?  7  ? 

15.  57  are  how  many  times  3  ? 

16.  60  are  how  many  times. 2  ?  3?  4?  5?  6? 

17.  64  are  how  many -times  2?  4  ?  8? 

18.  66  are  how  many  times  2  ?  3  ?  6  ? 

19.  68  are  how  many  times  2  ?  4  ? 

20.  70  are  how  many  times  10?  2? 

21.  72  are  how  many  times  2  ?  4?  6  ?  8  ? 

22.  5  are*  how  many  times  2,  and  how  many  je^ 
maining  ? 


Remark. — 'Whenever  there  is  a 
tioned  simply  as  a  remainder. 

23.  7  are  how  many  times 

24.  17  are  how  many  times 

25.  18  arc  how  many  times 

26.  34  are  how  many  times 

27.  25  are  how  many  times 

28.  16  are  how  many  times 

29.  32  are  how  many  times 

30.  63  are  how  many  times 

31.  74  are  how  many  times 


remainder,  it  may  be  men- 


2? 

4? 

2? 

5? 

6? 

4  ? 

2? 

4? 

6? 

5? 

2? 

5? 

4? 

2? 

3? 

9? 

4? 

8? 

7? 

7? 

5? 

6? 

9? 

4? 

5? 

6? 

2? 

4? 

6? 

7? 

40 


DIVISION. 


32. 

33. 

34. 

35. 


36. 

37. 


80  are  how  many  times  2  ?  3  ?  4  ? 

84  are  how  many  times  2  ?  3  ?  4  ? 

15  are  how  many  times  4  ?  6  ?  7  ? 

29  are  how  many  times  2  ?  3  ?  4  ? 

90  are  how  many  times  2  ?  4  ?  6  ? 

144  are  how  many  times  2  ?  4  2  6 


5?  6?  7?  8? 
5?  6?  7  ?  8? 
8? 

5  ?  6?  7? 

8?  9*  11  ? 

?  8?  12? 


— _ — »♦•»• - - - 

/ 

LESSON  III. 

1.  At  2  cents  each,  how  many  lemons  can  you  buy 
for  14  cents? 

Solution. — If  1  lemon  cost  2  cents,  for  14  cents  I  can  buy 
as  many  lemons  as  2  is  contained  times  in  14,  which  are  7. 

Another  Solution.— If  for  2  cents  I  can  buy  1  lemon,  for  1 
cent  I  can  buy  1  half  of  a  lemon,  and  for  14  cents,  14  times  1 
half,  which  are  14  halves,  or  7  lemons. 

2.  How  many  boxes  of  cheese,  at  4  dollars  a  box, 

may  be  had  for  12  dollars? 

3.  If  one  hundred  pounds  of  hay  cost  3  dollars,  how 
many  hundred  may  be  had  for  15  dollars  ? 

4.  If  one  barrel  of  flour  support  20  persons  one 
week,  how  many  persons  will  it  support  4  weeks  ? 

5.  If  1  man  can  ride  1  mile  for  4  cents,  how  far 

can  2  men  ride  for  80  cents  ? 

6.  If  10  men  accomplish  a  certain  piece  of  work  in 
2  days,  how  long  will  it  take  1  man  to  do  the  same  ? 

7.  If  3  yards  of  cloth  make  one  coat,  how  manj 

coats  will  18  yards  make? 

8.  If  I  receive  12  dollars  interest  in  one  year,  in 
how  many  years  will  I  receive  144  dollars  interest  ? 

9.  A  man  traveled  7  miles  in  1  hour,  at  the  same 
rate,  how  long  would  it  take  him  to  travel  63  miles  ? 

10.  If  1  cow  cost  13  dollars,  how  many  cows  may 
be  had  for  65  dollars  ? 

11.  How  many  pens  can  you  buy  for  27  cents,  if  1 
pen  cost  3  cents  ? 


MULTIPLICATION  AND  DIVISION.  41 


12.  If  8  apples  are  worth  40  chestnuts,  how  many 
chestnuts  is  1  apple  worth  ? 

13.  How  many  cents  is  1  lemon  worth,  if  12  lemons 
are  worth  48  cents  ? 

14.  How  much  will  1  cord  of  wood  cost,  if  20  cords 
cost  40  dollars  ? 

15.  If  1  pound  of  beef  cost  7  cents,  how  much  will 
19  pounds  cost  ? 

16.  For  147  cents,  how  many  pounds  of  sugar  can 
be  bought,  at  7  cents  a  pound  ? 

17.  If  9  yards  of  cloth  cost  53  dollars,  for  how 
much  must  it  be  sold  a  yard  to  gain  10  dollars  ? 

18.  If  7  barrels  of  flour  cost  38  dollars,  and  were 
sold,  at  7  dollars  a  barrel,  what  was  the  gain  ? 

19.  How  many  peaches,  at  4  cents  each,  may  be 
bought  for  96  cents  ? 

20.  How  many  yards  of  cloth,  at  4  dollars  a  yard, 
can  be  bought  for  116  dollars? 

21.  How  many  oranges,  at  3  cents  each,  must  be 
given  for  1 8  lemons  worth  4  cents  each  ? 

22.  If  15  sheep  cost  75  dollars,  what  will  1  sheep 
cost  ? 

23.  Which  will  cost  the  most,  4  barrels  of  wheat 
flour,  at  9  dollars  a  barrel,  or  12  barrels  of  corn,  at  4 
dollars  a  barrel,  and  how  much  ? 

24.  How  many  barrels  of  beef,  at  3  dollars  a  barrel, 
can  be  bought  for  54  dollars  ? 

25.  How  many  pounds  of  fish,  at  5  cents  a  pound, 
may  be  had  for  95  cents  ? 

26.  At  7  cents  a  pound,  how  many  pounds  of  lead 
may  be  had  for  84  cents  ? 

27.  How  long  will  it  require  to  travel  105  miles,  at 
the  rate  of  5  miles  an  hour  ? 

28.  A  person  divided  72  peaches  equally  among  6 
boys ;  how  many  did  each  receive  ? 

29.  148  marbles  were  divided  equally  among  some 


42  MULTIPLICATION  AND  DIVISION. 

boys  ;  bow  many  boys  were  there,  provided  each  boy 
received  2  marbles? 

30.  How  many  pounds  of  butter,  at  14  cents  a 
pound,  can  be  bought  for  28  apples,  at  3  cents  each  ? 

31.  At  7  cents  a  bottle,  how  many  bottles  of  ink  can 
you  buy  for  14  sheets  of  paper,  at  2  cents  a  sheet  ? 

32.  In  how  many  days  can  1  man  do  as  much  as  7 
men  in  8  days  ? 

33.  In  how  many  days  can  2  men  do  as  much  work 
as  6  men  in  3  days  ? 

34.  In  how  many  days  can  4  men  earn  as  much  as 
8  men  in  6  days  ? 

35.  In  how  many  days  can  15  men  earn  as  much 
as  3  men  in  25  days? 

36.  In  how  many  months  will  6  horses  eat  as  much 
as  18  horses  in  5  months? 

37.  How  many  men  can  in  7  days  earn  as  much  as 

28  men  in  4  days  ?  ! 

38.  In  10  days  6  men  will  earn  as  much  as  how 
many  men  in  5  days  ? 

39.  How  many  yards  of  cloth,  at  4  dollars  a  yard, 
may  be  had  for  4  sets  of  chairs,  at  12  dollars  a  set  ? 

40.  A  farmer  gave  13  barrels  of  flour,  worth  4  dol¬ 
lars  a  barrel,  for  26  yards  of  cloth  \  how  much  was 
the  cloth  a  yard  ? 


- - - 

LESSON  IV. 

CHAPTERS  FIRST,  SECOND,  THIRD,  AND  FOURTH  COMBINED. 

1.  4  times  6  are  how  many  times  2  ? 

Solution. — 4  times  6  are  24.  24  are  12  times  2.  Therefore, 

4  times  6  are  12  times  2. 

2.  4  times  9  are  how  many  times  3  ? 

3.  4  times  8  are  how  many  times  2  ? 


\ 


FUNDAMENTAL  RULES.  43 

4.  4  times  10  are  how  many  times  5  ? 

5.  4  times  12  are  how  many  times  6  ? 

6.  4  times  14  are  how  many  times  7  ? 

7.  5  times  9  are  how  many  times  15  ? 

8.  5  times  8  are  how  many  times  4  ? 

9.  5  times  12  are  how  many  times  15  ?  6? 

10.  6  times  7  are  how  many  times  2  ? 

11.  6  times  8  are  how  many  times  12  ?  3? 

12.  4  times  6  are  how  many  times  8? 

13.  7  times  15  are  how  many  times  5  ? 

14.  12  times  7  are  how  many  times  21  ? 

15.  8  times  7  are  how  many  times  4? 

16.  How  many  times  12  are  9  times  4  ? 

17.  How  many  times  20  are  5  times  4? 

18.  How  many  times  9  are  3  times  21,  +9  ? 

19.  How  many  times  5  are  7  times  15,  +10  —  5  ? 

20.  How  many  times  9  are  3  times  36,  —  2  +  11  ? 

21.  How  many  times  12  are  9  times  4,  +24  —  12? 

22.  How  many  times  21  are  9  times  14,  +42  ? 

23.  How  many  times  7  are  3  times  14,  +21  — 14? 

24.  How  many  times  5  are  8  times  10,  +5  — 15  ? 

25.  How  many  times  5  arc  10  times  6,  +15  +  5? 

26.  How  many  times  5  are  6  times  15,  +10  +  15  ? 

27.  10  times  4,  +  2  are  how  many  times  7  ?  2  ? 

28.  8  times  9,-2  are  how  many  times  5  ? 

29.  12  times  8,-8  are  how  many  times  2  ? 

30.  26  times  11,  —  6  are  how  many  times  28  ? 

31.  7  times  8,  +  4  are  how  many  times  12  ? 

32.  6  times  7,  +  4  are  how  many  times  2  ? 

33.  5  times  8,  +  8  are  how  many  times  6  ? 

34.  4  times  9,  —  4  are  how  many  times  8  ? 

35.  9  times  5,  —  3  are  how  many  times  7  ? 

36.  7  times  12,  —  14  +  5  are  how  many  times  5? 

37.  4  times  15,  +  7  —  3  are  how  many  times  8  ? 

38.  6  times  7,  +  14  —  2  are  how  many  times  9  ? 

39.  11  times  13,  +  11  —  14  are  how  many  times  7  ? 

40.  11  times  15,  —  10  +  15  are  how  many  times  17  ? 


44 


SIMPLE  PROPORTION. 


LESSON  V. 


PRACTICAL  QUESTIONS  COMBINING  CHAPTERS  THIRD  AND  FOURTH. 

1.  If  2  apples  cost  4  cents,  how  much  will  3  apples 
o  cost  ? 

Solution. — If  2  apples  cost  4  cents,  1  apple  will  cost  1  half  of 
4  cents,  which  is  2  cents.  If  1  apple  costs  2  cents,  3  apples  will 
cost  3  times  2  cents,  which  are  6  cents. 

2.  If  2  pears  cost  1 6c.,  how  much  will  5  pears  cost  ? 

3.  If  4  quinces  cost  12  cents,  how  much  will  3 
quinces  cost  ? 

4.  If  6  oranges  cost  18  cents,  how  much  will  9 
oranges  cost  ? 

5.  If  7  peaches  cost  21  cents,  how  much  will  9 
peaches  cost  ? 

6.  If  4  lemons  cost  24  cents,  how  much  will  7 
lemons  cost  ? 

7.  If  3  yards  of  tape  cost  18  cents,  how  much  will 

6  yards  cost? 

8.  If  7  hair-brushes  cos"|  28  dimes,  how  many  cents 
will  6  hair-brushes  cost? 

9.  If  9  yards  of  muslin  cost  108  cents,  how  much 
will  7  yards  cost  ? 

10.  If  11  books  cost  44  dimes,  how  many  cents  will 

7  books  cost? 

11.  If  12  ink-stands  cost  96  cents,  what  will  2  cost  ? 

12.  If  10  lead-pencils  cost  30  cents,  how  much  will 
be  the  cost  of  7  ?  of  9  ?  of  2  ?  of  1 5  ?  of  1 2  ? 

13.  How  much  will  13  yards  of  silk  cost,  if  5  yards 
cost  45  dimes  ? 

14.  If  a  man  travel  15  miles  in  3  hours,  how  far,  at 
this  rate,  can  he  travel  in  9  hours  ?  5  hours  ?  7  hours  ? 

15.  If  the  cartage  of  a  load  of  plaster  20  miles  cost 
4  dollars,  how  far  could  it  be  carried  for  1 2  dollars  ? 

16.  How  many  pair  of  pantaloons  can  be  cut  out  of 
21  yards  of  cloth,  if  3  pair  can  be  cut  out  of  9  yards 
of  the  same  kind  of  cloth  ? 


SIMPLE  PROPORTION. 


45 


17.  How  mueli  will  30  pounds  of  sugar  cost,  if  6 
pounds  cost  42  cents  ? 

18.  How  much  will  18  pounds  of  veal  cost,  if  6 
pounds  cost  42  cents? 

19.  How  much  will  75  pounds  of  pork  cost,  if  9 
pounds  cost  75  cents? 

20.  How  much  will  20  weeks’  board  amount  to,  if  7 
weeks’  board  cost  14  dollars? 

21.  How  much  will  be  the  wages  for  1  year,  if  4 
months’  wages  amount  to  48  dollars  ? 

22.  How  much  will  be  the  cost  of  25  bushels  of 
apples,  if  13  bushels  cost  260  cents? 

23.  How  much  will  14  pounds  of  cheese  cost,  if  6 
pounds  cost  54  cents? 

•  24.  If  7  quarts  of  milk  cost  35  cents,  how  much 

will  36  quarts  cost?  / 

25.  If  4  men  can  do  a  certain  piece  of  work  in  12 
days,  in  how  many  days  will  3  men  do  the  same 
work  ? 

26.  I  gave  72  dollars  for  a  quantity  of  cotton,  and 
*  sold  it  for  12  yards  of  cloth;  how  much  did  the  cloth 

cost  me  a  yard  ? 

27.  Gave  15  pounds  of  sugar  for  5  pounds  of  but¬ 
ter  ;  how  much  did  the  butter  cost  a  pound,  provided 

8  pounds  of  sugar  were  worth  56  cents?  . 

28.  If  4  chestnuts  are  worth  8  walnuts,  how  many 
walnuts  are  27  chestnuts  worth? 

29.  If  7  yards  of  broadcloth  are  worth  35  dollars, 
how  many  boxes  of  butter,  at  3  dollars  a  box,  would 

9  yards  of  this  cloth  buy  ? 

30.  A  man  bought  4  barrels  of  flour  for  20  dollars, 
and  gave  3  of  them  for  cider,  at  3  dollars  a  barrel ; 
how  many  barrels  of  cider  did  he  get  ? 

31.  A  man  bought  14  barrels  of  cider  for  56  dol¬ 
lars,  and  gave  5  barrels  of  it  for  cloth,  at  2  dollars  a 
yard ;  how  many  yards  did  he  receive  ? 

32.  A  merchant  having  15  yards  of  cloth  worth  75 


46 


SIMPLE  PROPORTION. 


dollars,  gave  10  of  them  for  pork,  worth  10  dollars  a 
barrel ;  how  many  barrels  did  he  receive  ? 

33.  When  9  bushels  of  rye  were  worth  45  dimes, 
12  bushels  were  given  for  15  yards  of  cloth;  how 
much  did  the  cloth  cost  a  yard  ? 

34.  If  35  yards  of  cloth  cost  140  dollars,  how  much 
will  95  yards  of  the  same  cloth  cost  ? 

35.  Two  boys  are  32  rods  apart, *and  both  running 
in  the  same  direction,  the  hindermost  boy  gains  on  the 
other  4  rods  each  minute ;  in  how  many  minutes  will 
he  overtake  him? 

36.  How  many  boxes  will  be  required  to  contain 
56  bushels,  provided  each  box  contains  8  bushels? 

37.  How  many  barrels  of  onions,  at  3  dollars  a  bar¬ 
rel,  must  be  given  for  21  boxes  of  raisins,  at  2  dollars 
a  box  ? 

38.  A  farmer  bought  9  yards  of  cloth,  at  4  dollars 

a  yard,  and  paid  for  it  with  cider,  at  3  dollars  a  barrel ; 
how  many  barrels  did  it  take  ?  ' 

^  39.  How  long  would  it  take  a  man  to  lay  up  24 
dollars,  if  he  save  2  dollars  a  week  ? 

40.  A  farmer  hired  a  laborer  and  agreed  to  give 
him  6  dollars  for  every  3  days’  work;  how  much  did 
he  receive  a  week,  allowing  6  working  days  in  a 
week?  how  much  a  month,  allowing  4  weeks  to  the 
month  ? 

41.  If  4  oranges  are  worth  12  cents,  how  many 

oranges  must  be  given  for  6  pine-apples,  worth  12 
cents  each  ?  . 

42.  How  many  yards  of  cloth,  at  2  dollars  a  yard, 
can  be  bought  for  4  reams  of  paper,  at  5  dollars  a 
ream  ? 

43.  6  men  bought  a  horse  for  80  dollars,  and  paid 
2  dollars  a  week  for  keeping  him  ; — at  the  end  of  10 
weeks  they  sold  him  for  82  dollars ;  how  much  did 
each  man  lose  ? 

44.  If  2  apples  are  worth  1  orange,  and  2  oranges 


TABLES  AND  REDUCTION. 


47 


are  worth  1  lemon  ;  how  many  lemons  can  he  bought 
for  48  apples  ? 

45.  If  5  oranges  are  worth  1  pine-apple,  and  2  pine¬ 
apples  are  worth  1  melon  ;  how  many  oranges  may  be 
bought  for  4  melons  ? 

46.  A  fox  is  80  rods  before  a  hound,  and  the  hound 
gains  5  rods  on  the  fox  every  10  minutes  ;  in  how 
many  minutes  will  the  fox  be  caught  ? 

47.  If  7  men  can  do  a  certain  job  of  work  in  12 
days,  in  how  many  days  could  21  men  do  the  same 
work?  - 

48.  In  how  many  days  can  9  men  do  as  much  work 
as  7  men  can  in  18  days? 

49..  How  many  men  in  10  days  can  perform  the 
same  amount  of  work,  that  8  men  can  in  5  days? 

50.  Bought  5  firkins  of  butter  for  35  dollars  ;  for 
what  must  I  sell  it  to  gain  10  dollars  ?  what  is  the  gain 
on  each  firkin  ? 

- » - 

CHAPTER  Y. 

LESSON  I. 

Table  op  United  States  Currency. 

10  Mills  (m.)  make  1  Cent,  marked  c. 

10  Cents  “  1  Dime,  “  d. 

10  Dimes  “  1  Dollar,  u  $. 

10  Dollars  “  1  Eagle,  «  E. 

1.  How  many  mills  in  4  cents  ? 

Solution. — In  1  cent  there  are  10  mills,  and  in  4  cents  there 
are  4  times  10  mills,  or  40  mills. 

2.  How  many  mills  in  3  cents?  In  5  cents?  In  8 
cents  ? 

3.  How  many  cents  in  2  dimes  ?  In  4  dimes  ?  In 
5  dimes?  In  6  dimes?  In  9  dimes?  In  10  dimes? 


48 


TABLES  AND  REDUCTION. 


4.  How  many  dimes  in  $1  ?  In  $2  ?  In  $3  ?  In 

$4  ?  In  $5  ?  In  $6  ? 

5.  How  many  dimes  in  1  eagle  and  $4?  In  2  eagles 
and  $8  ? 

6.  How  many  cents  in  $1  ?  In  $2  ?  In  $3?  In 
$4  ?  In  $5  ?  In  $8  ? 

7.  How  many  dollars  in  80  dimes  ? 

Solution. — There  are  10  dimes  in  $1,  therefore,  1  tenth  of 
the  number  of  dimes  equals  the  number  of  dollars.  1  tenth  of 
80  is  8.  Therefore,  in  80  dimes  there  are  $8. 

8.  How  many  dimes  in  60  cents?  In  70  cents? 
In  90  cents  ? 

9.  How  many  dollars  in  200  cents?  In  500  cents  ? 
In  800  cents?  In  360  cents?  In  705  cents? 

10.  If  3  yards  of  muslin  cost  6  dimes,  how  many  • 
yards  can  be  bought  for  1  dollar  ? 

11.  How  many  pounds  of  pepper  can  you  buy  for 
1  eagle,  if  12  pounds  cost  6  dimes?  T 

12.  How  many  pounds  of  candies  can  you  buy  for 
14  eagles,  if  10  pounds  cost  140  cents  ?  [  g  >-■ 


LESSON  II. 


Table  op  English  Money. 

4  Farthings  (far.)  make  1  Penny,  marked  d. 

12  Pence  “  1  Shilling,  “  s. 

20  Shillings  “  1  Pound  “  £. 

A  Sovereign  ( sov .)  is  equal  in  value  to  1£. 

1.  How  many  shillings  in  4£  15  shillings? 

Solution. — There  are  20  shillings  in  1£,  therefore,  20  times 
the  number  of  pounds  equal  the  number  of  shillings.  20  times 
4  are  80  shillings  +15,  are  95  shillings. 

2.  How  many  pence  in  1  shilling?  In  4  shillings? 
In  3  shillings?  In  7  shillings?  In  9  shillings? 

3.  How  many  shillings  in  l£  ?  In  2£?  In  3£  ? 
In  6£  ? 


TABLES  AND  REDUCTION. 


49 


4.  How  many  pence  in  2£  10  shillings  5  pence? 

5.  How  many  pounds  in  60  shillings  ?  In  80s.  ? 
In  120s.  ? 

6.  How  many  pounds  in  480  pence  ?  In  7200?.  ? 

7.  At  4  shillings  a  bushel,  how  many  pounds  will 
40  bushels  of  potatoes  cost  ? 

8.  At  10  pence  a  piece,  how  many  pounds  will  48 
pine-apples  cost  ? 

9.  At  5  shillings  a  yard,  how  many  yards  of  cloth 
can  be  bought  for  2£  15  shillings  ? 


v\ 

oJ 


LESSON  III. 


Table  of  Troy  Weight. 


24  Grains  ( gr .) 

20  Pennyweights 
12  Ounces 


make  1  Pennyweight,  marked  pwt. 
“  1  Ounce,  “  oz. 

“  1  Pound,  “  lb. 


1.  How  many  pennyweights  in  240  grains? 

2.  How  many  pennyweights  in  4  ounces  ?  In  5 
ounces  ?  In  6  ounces  ? 

3.  How  many  ounces  in  1  pound  ?  In  3  pounds  ? 
In  5  pounds  ?  In  8  pounds  ? 

4.  In  24  ounces  how  many  pounds  ?  In  48  ounces  ? 
In  36  ounces  ?  In  60  ounces  ?  In  84  ounces  ? 

5.  How  many  ounces  in  20  pennyweights  ?  In  40  ? 
In  60  ?  In  70  ? 

6.  If  7  grains  of  gold  cost  168  dimps,  how  much 
will  10  pennyweights  cost? 

7.  What  will  1  pennyweight  of  gold  cost,  if  2 
grains  cost  18  dimes?  / /(j 

8.  How  many  pennyweights  in  4  ounces  and  6 
pennyweights  ? 

9.  How  many  pounds  in  480  pennyweights  ? 

10.  How  many  grains  in  2  oz.,  2  pwt.,  and  2  gr. 

5 


50 


TABLES  AND  DEDUCTION. 


LESSON  IV. 


Table  of  Avoirdupois  Weight. 

16  Drams,  (dr.)  make  1  Ounce,  marked  oz. 

16  Ounces  “  1  Pound,  “  lb. 

25  Pounds  “  1  Quarter,  “  qr. 

4  Quarters,  or  100  lbs.  “  1  Hundred-weight,  “  cwt. 

20  Hundred-weight,  “  1  Ton,  “  71 

1.  How  many  drams  in  2  oz.  ?  In  4  oz.  ?  In  10  oz.  ? 

2.  How  many  ounces  in  2  lbs.  ?  In  4  lbs.  ?  In  8  lbs.  ? 

3.  How  many  quarters  in  100  pounds?  in  400 
pounds?  in  600  pounds?  in  1200  pounds? 

4.  How  many  pounds  in  3  qrs.  ?  In  2  qrs.  ?  In  7  qrs,  ? 

5.  How  many  quarters  in  2  hundred- weight  ?  " 

6.  In  8  quarters  how  many  hundred-weight? 

7.  If  30  lbs.  of  hay  cost  6  dimes,  what  will  3  quar¬ 
ters  cost  ?  will  1  cwt.  ?  will  2  cwt.  and  1  qr.  ?  . 

8.  What  will  2  tons  of  iron  cost,  if  1  lb.  cost  1 
dime  ? 

9.  What  will  40  tons  of  hay  cost,  at  2  dimes  a  qr.  ?  -  - 

10.  What  will  2  cwt.  of  sugar  cost,  at  a  dime  a 

pound  ?  at  5  cents  a  pound  ?  g  ' 

‘ 

- — o-  - 


LESSON  V. 


Table  of  Long  Measure. 


12  Inches  (in.)  make  1 

3  Peet  “  1 

5 1  Yards,  or  16|  feet  “  1 

40  Rods  “  1 

8  Furlongs,  or 320  rods,  “  1 

3  Miles  “  1 

69j  Miles  “  1 

360  Degrees  “  1 

1.  How  many  inches  ii 
In  5  ft.  ?  In  10  ft.  ? 


Foot, 

marked  ft. 

Yard, 

il 

yd. 

Rod, 

«( 

rd. 

Furlong, 

ii 

fur. 

Mile 

it 

mi. 

League, 

n 

lea. 

Degree,  “ 

Circle  of  the  earth. 

deg.  or  °. 

1  ft.? 

In  2  ft.  ? 

In  4  ft.  ? 

TABLES  AND  REDUCTION. 


51 


2.  How  many  feet  in  2  yds.  ?  In  6  yds.  ?  In  5  yds.? 
In  12  yds.  ? 

3.  How  many  yards  in  2  rods  ?  In  4  rds.  ?  In  8 
rds.?  In  10  rds? 

4.  How  many  furlongs  in  4  miles  ?  In  6  mi.  ?  In 
9  mi.  ? 

5.  How  many  inches  4  yds.  2  ft.  10  in.  ? 

6.  In  216  inches,  how  many  yards?  In  288  in.  ? 

7.  How  many  rods  in  1  mile  ? 

8.  How  many  miles  in  1760  yards  ?  ' 

9.  How  many  feet  in  2  rods,  3  yds.,  2  ft.,  11  in.  ? 

10.  How  many  feet  in  1  mile  ? 

- «»>«»..> - ■ 


no  / 

LESSON  VI. 


Table  of  Cloth  Measube. 


24  Inches 

make 

i 

Nail, 

Quarter  of  a  yard, 

marked 

na. 

4 

Nails 

a 

i 

U 

qr . 

4 

Quarters 

u 

i 

Yard, 

u 

yd. 

3 

Quarters 

u 

i 

Ell  Flemish, 

u 

E.  FI. 

5 

Quarters 

u 

i 

Ell  English, 

u 

E.  E._ 

6 

Quarters 

u 

i 

Ell  French, 

u 

E.  Fr. 

1.  In  4  yds.  3  qrs.,  how  many  quarters  ? 

2.  In  7  yds.  2  qrs.,  how  many  Ells  French  ? 

3.  In  3  yds.  3  qrs.,  how  many  Ells  Flemish  ? 

4.  In  8  Ells  English,  how  many  yards  ? 

5.  In  7  Ells  Flemish,  how  many  yards  and  quarters  ? 

6.  In  3  Ells  French,  how  many  yards  and  quarters  ? 

7.  In  4  Ells  Fr.,  and  8  Ells  FI.,  how  many  yards  ? 

8.  In  1  qr.,  how  many  inches? 

9.  What  will  6  E.  E.  of  cloth  cost,  if  6  nails  cost 
48  cents  ? 

10.  What  will  3  E.  E,  +  2  E.  Fr.  of  cloth  cost,  if 
3  nails  cost  12  cents  ? 


TIMERS  t«0F 

tumois  ubrmn 


52 


TABLES  AND  KEDUOTION. 


LESSON  VII. 


Table  of  Land  oil  Square  Measure. 


144  Square  inches,  (sq.  in.) 
9  Square  feet 
30^  Square  yards 
40  Square  rods 
4  Roods 
640  Acres 


make 

1  Square  foot, 

1  Square  yard, 

sq.ft. 

U 

sq.  yd. 

U 

1  Square  rod,  or 

pole,  P. 

u 

1  Rood, 

B. 

u 

1  Acre, 

A. 

u 

1  Square  mile, 

sq.  m. 

1.  How  many  square  feet  in  4  sq.  yds.  ?  In  8 
sq.  yds.  ? 

2.  How  many  poles  in  4  roods  ?  In  0  roods  ? 

3.  How  many  acres  in  40  roods?  In  160  roods? 

4.  How  many  square  yards  in  81  sq.  ft.?  In  108 
sq.  ft.  ? 

5o  How  many  square  }rards  in  1  rood  10  rods  ? 


»♦» 


LESSON  VIII. 


Table  of  Cubic  Measure. 


1128  Cubic  inches  (cu.  in.) 
27  Cubic  feet 
24|  Cubic  feet 
16  Cubic  feet 
8  Cord  feet,  or  ) 

128  Cubic  feet  J 


make  1  Cubic  foot,  cu.  ft. 

11  1  Cubic  yard,  cu.  yd. 

“  1  Perch  of  stone,  pch. 

“  1  Cord  foot,  c.  ft. 

“  1  Cord  of  wood,  0. 


1.  How  many  cubic  feet  in  4  cubic  yards? 

2.  How  many  cubic  feet  in  4  perch  of  stone  ? 

3.  How  many  cords  in  96  cord  feet?  In  72  c.  ft.? 

4.  How  many  cords  in  128  cu.  ft.?  In  384  cubic 
feet? 

5.  How  many  cord  feet  in  4  cords  ?  In  6  cords ? 
In  9  cords? 


TABLES  AND  REDUCTION. 


53 


4 

Gills  (gi.) 

LESSON  IX. 

Table  oi*  Wine  Measure. 

make  1  Pint, 

marked  pt. 

2 

Pints 

a 

1  Quart, 

a 

qt. 

4 

Quarts 

a 

1  Gallon, 

a 

gal. 

42 

Gallons 

a 

1  Tierce, 

a 

tier. 

314  Gallons 

a 

1  Barrel, 

a 

bar. 

2 

Bar.  or  63  Gallons  “ 

1  Hogshead, 

a 

hhd. 

2 

Hogsheads 

a 

1',  u 

1  Pipe, 

a 

pi. 

2 

Pipes 

1  !Tun, 

a 

tun. 

1.  How  many  gills  in  3  pints  ?  In  4  pints? 

2.  In  3  qts.,  hqw  many  gills  ? 

3.  In  12  gallons,  how  many  pints? 

4.  What  will  5  gal.  of  rum  cost,  if  4  gi.  cost  5  cents? 

5.  How  many  pints  in  2  pipes? 

6.  A  merchant  bought  a  hogshead  of  molasses  for 
20  dollars,  and  sold  it,  at  the  rate  of  15  cents  for  3 
pints  ;  how  much  did  he  gain  by  the  bargain  ? 

7.  How  much  will  a  gallon  of  wine  cost,  if  7  gills 
cost  21  cents  ? 

8.  In  1  tierce,  how  many  pints  ? 

9.  In  4  quarts  and  2  pints,  how  many  gills  ? 

10.  In  1  tun,  how  many  gills  ? 

11.  In  1  barrel,  how  many  pints? 

-  <!»♦'«<» 


LESSON  X. 


Table  of  Dey  Measure. 

2  Pints  make  1  Quart,  marked  qt. 

8  Quarts  “  1  Peck,  “  pk. 

4  Pecks  “  1  Bushel,  “  bu. 

1.  In  1  peck  how  many  pints  ? 

2.  2  pecks  will  fill  how  many  pint  measures  ? 

3.  In  3  pecks  and  3  quarts  how  many  pints  ? 


54 


TABLES  AND  REDUCTION. 


4.  In  1  bushel  and  3  pecks,  how  many  quarts  ? 

5.  In  1  bushel,  how  many  quarts  ?  how  many 
pints  ? 

6.  If  8  pints  of  nuts  cost  24  cents,  what  will  3  pecks 
cost  at  the  same  rate?  */  ■ 

7.  A  market  woman  bought  4  quarts  of  strawber¬ 
ries  for  29  cents,  and  sold  them,  at  5  cents  a  pint;  how 
much  did  she  gain  ? 

8.  A  person  sold  2  bushels  and  1  peck  of  currants, 

at  2  cents  a  pint,  and  in  payment  received  1  bushel  of 
gooseberries,  at  4  cents  a  pint;  how  much  remains 
due  ?  -  -  :l 

9.  What  will  5  quarts  of  wheat  cost,  if  1  bushel 
cost  128  cents? 

10.  A  farmer  sold  1  bu.,  3  pk.  and  1  pt.  of  clover- 
seed,  at  640  cents  a  bushel,  and  in  payment  received 
1  bu.,  2  pk.  and  3  quarts  of  grass-seed,  at  320  cents  a 
bushel ;  how  much  remains  due  ? 

• — — — — ^ - - 

LESSON  XI. 


Table  of  Time. 


60 

Seconds  (sec.) 

make 

1  Minute,  marked 

on. 

60 

Minutes 

U 

1  Hour, 

66 

hr. 

24 

Hours 

u 

1  Day 

66 

d. 

1 

Days 

u 

1  Week, 

u 

w. 

4 

Weeks 

u 

1  Month, 

66 

mo. 

12 

Calendar  months 

u 

1  Year, 

u 

yr. 

52 

Weeks 

u 

1  Year, 

1  Common  Year, 

u 

yr. 

365 

Days 

u 

u 

yr. 

366 

Days 

16 

1  Leap  Year, 

u 

yr. 

100 

Years 

u 

1  Century, 

16 

G. 

The  following  table  exhibits  the  divisions  of  the  year, 
the  names  of  the  months,  and  the  number  of  days  in 
each : — 


TABLES  AND 


EEDUCTIO N. 


55 


I J 

>  1st  month,  January, 

has 

31  days. 

£  < 

|  2d 

u 

February, 

tt 

28, 

in  leap  year  29, 

i 

;  3d 

u 

March, 

April, 

it 

31  days. 

■g  \ 

4th 

a 

it 

30 

U 

Ph  i 

1 

[  5th 

u 

May, 

tt 

31 

tt 

<D  \ 

[  6th 

u 

June, 

July, 

It 

30 

tt 

!< 

7  th 

u 

it 

31 

it 

i  l 

Ul 

[  8th 

ti 

August, 

it 

31 

it 

i  < 

[  9  th 

tt 

September, 

tt 

30 

it 

1 1 

10  th 

u 

October, 

a 

31 

u 

<  ’ 

[  11th 

u 

November, 

a 

30 

tt 

U  i 
1 

[  12th 

it 

December, 

tt 

31 

a 

S3 

£ 


The  following  lines  will  help  to  remember  the  num¬ 
ber  of  days  in  each  month  : 

“Thirty  days  hath  September, 

April,  June,  and  November; 

February  twenty-eight,  alone, 

All  the  rest  have  thirty-one, 

Except  in  Leap  Year ;  then  is  the  time 
When  February  has  twenty-nine.” 

|W°  In  our  calculations  on  interest  we  shall  reckon  30  days  to 
the  month ,  and  12  months  to  the  year ,  although  not  strictly  accu¬ 
rate. 

% 

1.  In  2  hours  how  many  seconds? 

2.  In  2  weeks  and  5  days,  how  many  days  ? 

3.  In  48  hours,  how  many  days  ? 

4.  7200  seconds,  how  many  hours? 

5.  How  many  hours  in  a  week  ? 

6.  In  1  day,  12  hours  and  10  minutes;  how  many 

minutes  ?  > 

7.  How  many  hours  in  a  month  ? 

8.  If  a  boy  can  do  a  piece  of  work  in  40  minutes, 
how  many  hours  would  it  take  him  to  perform  12 
times  as  much  work  ?  ct'  . 


56 


FRACTIONS. 


9.  If  I  can  do  a  piece  of  work  in  10  minutes,  how 
many  hours  would  it  take  to  perform  a  piece  of  work 
12  times  as  large  ? 

10.  How  many  days  in  3  weeks  and  5  days? 


LESSON  XII. 

Miscellaneous  Table. 


12  Units 

make  1  Dozen. 

12  Dozen 

U 

1  Gross. 

12  Gross 

U 

1  Great  Gross. 

20  Units 

u 

1  Score. 

24  Sheets  of  Paper 

u 

1  Quire. 

20  Quires 

a 

1  Ream. 

56  Pounds 

u 

1  Bushel  of  Corn. 

60  Pounds 

u 

1  Bushel  of  Wheat. 

196  Pounds 

u 

1  Barrel  of  Flour. 

(  1  Barrel  of  Beef, 

200  Pounds 

u 

(  Pork,  or  Fish. 

1.  What  will  2  reams 

of 

paper  cost,  at  15  ce 

quire 


2.  How  many  sheets  of  paper  in  1  ream  ? 

3.  How  many  years  in  “  3  score  years  and  10”  ? 

4.  How  many  units  in  a  gross  ? 

5.  How  many  units  in  6  dozen  dozen  ? 

6.  How  many  units  in  a  half  of  a  dozen  dozen  ? 


■il  M 


CHAPTER  YI. 

LESSON  I. 

1.  John  has  6  nuts,  and  Joel  1  half  as  many ;  how 
many  has  he  ? 

Solution. — If  John  has  6  nuts,  and  Joel  1  half  as  many,  Joel 
must  have  1  half  of  6,  or  3  nuts. 


•I'L'-'til  •  •  \  . 

•  ,  •  .  ••  •  ■  ■ 

'  .  .. 


FRACTIONS. 


57 


2.  Mary  had  4  dresses,  and  Rachel  1  half  as  many  ; 
how  many  had  she  ? 

3.  Jacob  is  8  years  old,  and  John  is  1  half  as  old  ; 
how  old  is  John  ? 

4.  Moses  having  2  marbles,  gave  1  half  of  them  to 
his  brother  ;  how  many  had  he  left? 

5.  If  you  divide  6  apples  equally  between  2  boys, 
what  part  of  them  will  each  have  ? 

6.  What  is  1  half  of  6  ? 

7.  How  many  halves  in  1  ? 

8.  If  an  orange  cost  8  cents,  and  a  peach  1  half  as 
much,  what  is  the  cOst  of  the  peach  ? 

9.  James  had  12  cakes,  and  John  1  half  as  many  ; 
how  many  had  John? 

10.  If  3  apples  cost  6  cents,  what  part  of  6  cents 
will  1  apple  cost? 

11;  What  is  1  third  of  6  ? 

12.  What  is  1  half  of  8  ?  10?  12?  14?  16?  18? 
20  ? 

13.  If  3  quarts  of  strawberries  cost  18  cents,  what 
part  of  18  cents  will  1  quart  cost?  What  part  of  18 
cents  will  2  quarts  cost  ? 

14.  What  is  1  third  of  18  ?  1  half  of  18  ? 

15.  If  4  pounds  of  raisins  cost  8  dimes,  what  part 
of  8  dimes  will  1  pound  cost  ?  2  pounds  ?  3  pounds  ? 
4  pounds?  5  pounds?  6  pounds? 

16.  What  is  1  fourth  of  8  ?  of  12  ?  of  16  ?  of  20  ? 

17.  What  is  1  fifth  of  15?  of  10?  of  20?  of  30? 

18.  If  1  fifth  of  15  is  3,  what  is  2  fifths  of  15?  3 
fifths?  4  fifths?  6  fifths?  8  fifths? 

19.  What  is  1  sixth  of  12? 

20.  If  1  sixth  of  12  is  2,  what  is  2  sixths  of  12?  3 
sixths?  4  sixths?  5  sixths?  7  sixths?  8  sixths? 

21.  What  is  1  seventh  of  21  ? 

22.  If  1  seventh  of  21  is  3,  what  is  2  sevenths  of  21  ? 
3  sevenths  ?  4  sevenths  ?  5  sevenths  ?  6  sevenths  ? 

23.  If  1  pound  of  candies  cost  12  cents,  what  part 


58 


FRACTIONS. 


of  a  pound  can  you  buy  for  1  cent  ?  for  2  cents  ?  for  3 
cents  ?  for  5  cents  ?  for  8  cents  ? 

24.  If  a  coat  cost  $20,  and  a  pair  of  pantaloons  1 
fourth  as  much,  how  much  will  the  pantaloons  cost  ? 

25.  If  7  barrels  of  cider  cost  $28,  what  part  of  $28 
will  1  barrel  cost  ?  4  barrels  ?  7  barrels  ?  5  barrels  ? 

26.  What  is  1  seventh  of  $28?  2  sevenths  of  $28? 
4  sevenths  ?  5  sevenths  ?  7  sevenths  ?  6  sevenths  ? 

27.  If  1  pound  of  cheese  cost  6  cents,  how  much 
will  1  third  of  a  pound  cost  ?  2  thirds  ? 

28.  If  12  lemons  cost  36  cents,  what  part  of  36 
cents  will  1  lemon  cost?  2  lemons?  4  lemons?  5 
lemons?  8  lemons?  10  lemons?  9  lemons?  7  lemons? 

29.  What  is  1  twelfth  of  36  ?  2  twelfths  of  36  ?  4 
twelfths?  5  twelfths?  6  twelfths?  9  twelfths?  10 
twelfths?  14  twelfths? 

30.  What  do  you  understand  by  1  third?  2  thirds? 

Answer. — When  a  thing  has  been  divided  into  three  equal 
parts,  1  of  these  parts  is  called  1  third,  and  2  of  these  parts  are 
called  2  thirds. 

31.  What  do  you  understand  by  1  half? 

32.  What  do  you  understand  by  1  fourth  ?  2  fourths  ? 
3  fourths  ? 

33.  What  do  you  understand  by  1  fifth?  2  fifths? 
3  fifths  ?  4  fifths  ? 

34.  How  many  thirds  make  a  whole  one  ? 

35.  How  many  fourths  in  1  ? 

36.  What  do  you  understand  by  2  sixths  ?  4  sixths  ? 

37.  What  do  you  understand  by  3  sevenths?  2 
sevenths?  4  sevenths?  5  sevenths? 

38.  How  many  sixths  in  1  ? 

39.  How  many  ninths  in  1  ? 

40.  How  many  eighths  in  1  ? 

41.  How  many  sevenths  in  1  ? 

42.  How  many  tenths  in  1  ? 

43.  How  many  twentieths  in  1  ? 


FRACTIONS. 


59 


44.  What  do  you  understand  by  7  twelfths?  6 
twelfths?  9  twelfths?  8  twelfths? 

45.  James  had  9  marbles,  and  Jacob  had  2  thirds 
as  many  ?  how  many  had  he  ? 

Solution. — If  James  has  9  marbles,  and  Jacob,  2  thirds  as 
many,  he  must  have  2  thirds  of  9  marbles.  1  third  of  9  is  3,  and 
2  thirds  are  2  times  3,  which  are  6  marbles,  Jacob’s  number. 

46.  Mary  bought  12  candies,  and  Sarah  bought  2 
thirds  as  many  ;  how  many  did  Sarah  buy  ? 

47.  Rachel  has  12  primers,  Mary  3  fourths  as  many, 
and  Anthony  2  thirds  as  many  as  Mary  ;  how  many 
have  Mary  and  Anthony  respectively  ? 

48.  Albert  is  15  years  old,  and  Ebenezer  is  4  fifths 
as  old ;  how  old  is  he  ? 

49.  Augustus  has  40  cents,  and  Augusta  has  5 
eighths  as  many  ;  how  many  has  she  ? 

50„  Morgan  had  36  marbles,  and  gave  4  sixths  of 
them  to  Martin  ;  how  many  did  he  give  to  Martin,  and 
how  many  had  he  left  ? 

51.  Moses  had  24  fire-crackers,  and  Nathan  has  7 
sixths  as  many  ;  how  many  has  he? 

52.  Mifflin  had  45  cents,  and  Matthew  had  5  ninths 
as  many ;  how  many  had  he  ? 

53.  Dubois  is  20  years  old,  and  his  father  is  9  fifths 
as  old  ;  what  is  his  father’s  age  ? 

54.  A  farmer  had  84  sheep,  and  a  wolf  killed  1 
third  of  them;  how  many  had  he  remaining? 

/  55.  In  a  certain  school  there  are  12  girls,  and  7 
fourths  as  many  boys  ; — required  the  number  of  boys, 
and  the  number  of  boys  and  girls  together. 

56.  In  a  certain  recitation  36  questions  were  asked, 
and  1  ninth  of  them  answered  wrong ;  how  many 
were  correctly  answered  ? 

57.  4  fifths  of  all  the  words  given  out  in  a  spelling 
lesson  were  spelled  correctly,  and  8  were  misspelled ; 
of  how  many  words  did  the  lesson  consist  ? 


60 


FRACTIONS. 


58.  Montgomery  bought  9  filberts  for  1  cent;  what 
part  of  a  cent  did  1  cost  ?  2  ?  3?  6?  7  ?  9? 

59.  A  horse  was  bought  for  $60,  and  sold  for  7  fifths 
of  what  it  cost;  how  much  was  the  gain?  2_ 

60.  A  received  $140  for  14  weeks’  labor,  and  paid 

1  fifth  of  it  for  board ;  how  much  did  he  save  each 
week?  o  , 

61.  How  many  are  4  fifths  of  75?  % 

62.  How  many  are  7  eighths  of  24  ?  / 

63.  Mr.  A’s  wife  is  40  years  old,  and  9  eighths  of  her 
age  equals  his  ;  what  is  his  age  ? 

64.  What  is  2  ninths  of  36  ?  4  ninths?  3  fourths? 
4  sixths  ?  5  sixths  ?  4  twelfths  ?  9  twelfths  ? 

65.  How  many  are  3  fourths  of  48  ?  4  sixths  ?  5 
eighths?  7  eighths?  6  eighths?  5  sixths?  2  thirds? 

66.  3  ninths  of  27  are  how  many?  4  ninths?  7 
ninths  ?  8  ninths  ?  2  thirds  ? 

67.  3  fourths  of  24  are  how  many  times  3  ? 

Solution. — 1  fourth  of  24  is  6,  and  3  fourths  are  3  times  6, 
or  18.  18  are  6  times  3. 

68.  5  sevenths  of  63  are  how  many  times  3  ? 

69.  3  eighths  of  64  are  how  many  times  6  ? 

70.9  thirds  of  1 8  are  how  many  times  3  ? 

71.  4  fifths  of  25  are  how  many  times  2  ? 

72.  6  ninths  of  18  are  how  manv  times  6  ? 

73.  7  ninths  of  90  are  how  many  times  2  ? 

74.  4  thirds  of  39  are  how  many  times  2  ? 

75.  15  seventeenths  of  34  are  how  many  times  6  ? 

76.  How  many  times  17  are  17  eighteenths  of  36  ? 

77.  How  many  times  8  are  12  thirteenths  of  26  ? 

78.  How  many  times  5  are  10  thirds  of  36  ? 

79.  How  many  times  4  are  2  thirds  of  27,  —  2  ? 

80.  How  many  times  6  are  3  halves  of  48,  4*  12  ? 

81.  Stephen  having  40  apples,  gave  3  fifths  of  them 
to  one  companion,  and  3  eighths  of  them  to  another ; 
how  many  had  he  remaining  ? 

82.  A  had  $120  ;  1  third  of  it  he  spent  for  a  watc'h, 


FRACTIONS. 


61 


1  fourth  of  it  for  a  suit  of  clothes,  and  3  tenths  of  it 
for  a  sleigh;  how  much  had  he  remaining? 

83.  Mr.  B,  being  asked  the  cost  of  his  hat,  replied, 

2  thirds  of  30  dollars  is  4  times  its  cost ;  required 
the  cost  of  the  hat  ? 

84.  14  ninths  of  $27  is  equal  to  7  times  the  cost  of 
a  pair  of  boots ;  required  the  cost  of  the  boots. 

85.  An  individual,  having  $90  on  interest,  received 
2  forty-fifths  of  the  principal  for  the  interest;  how 
much  interest  did  he  receive? 

86.  The  interest  received  on  $360,  was  1  eighteenth 
of  the  principal ;  how  much  was  the  interest  ? 

87.  B  is  worth  $2000,  and  3  fourths  of  his  fortune 
is  3  times  A’s  ;  required  A’s  fortune. 

88.  3  eighths  of  the  number  of  hours  in  a  day,  is  3 
times  the  number  of  hours  I  work ;  how  many  hours 
do  I  work  ? 

89.  A  pole,  whose  length  is  16  feet,  is  in  the  air 
and  water ;  and  3  fourths  of  the  whole  length, — 4  feet, 
equals  the  length  in  the  air ;  required  the  length  in 
the  water. 

—  90.  3  fifths  of  $2000,  +  $120,  equals  B’s  fortune; 
how  much  is  B  worth  ? 

91.  The  building  of  a  certain  house  cost  $560,  and 
4  sevenths  of  this,  +  $80,  is  1  tenth  of  the  cost  of  the 
farm  on  which  it  stands.  Required  the  cost  of  the 
farm  ? 

92.  5  eighths  of  72,  +■  13,  are  how  many  times  2  ? 

93.  The  interest  on  $960  for  5  years,  was  equal  to 
1  third  of  the  principal ;  how  much  was  the  yearly 
interest  ? 

•?  94.  What  will  2  thirds  of  12  pounds  of  coffee  cost, 
at  13  cents  a  pound  ?  /  ’  7 

95.  What  will  3  fourths  of  a  gallon  of  alcohol  cost, 

at  9  cents  a  pint  ?  >  • 

96.  AVhat  will  1  sixteenth  of  a  bushel  of  flax-seed 
cost,  at  5  cents  a  pint  ?  ^ 

6 


62 


FEACTI  ONS. 


97.  IIow  much  will  7  fifteenths  of  30  pine-apples 
cost,  at  2  dimes  each  ? 

98.  How  much  will  7  ninths  of  a  hogshead  of  mo¬ 
lasses  cost,  at  4  dimes  a  gallon  ? 

99.  How  many  cents  will  3  fifths  of  100  oranges 
cost,  at  1  half  dime  each  ? 

100.  If  1  pennyweight  of  gold  cost  $2,  how  much 
will  2  fifths  of  an  ounce  cost  ? 

101.  What  will  he  the  cost  of  2  thirds  of  36  pounds 
of  butter,  at  2  dimes  a  pound  ? 

102.  2  thirds  of  24,  +  3  fourths  of  16,  are  how 
many  times  7  ? 

103.  2  thirds  of  30,  -f  3  fifths  of  40,  are  how  many 
times  8  ? 

104.  3  sevenths  of  21,  +  3  eighths  of  40,  are  how 
many  times  6  ? 

105.  How  far  can  I  walk  in  3  eighths  of  a  day,  at 
the  rate  of  3  miles  an  hour  ? 

106.  If  Marcus  earn  1  dime  in  an  hour,  how  many 
cents  can  he  earn  in  3  eighths  of  a  day  ? 

107.  If  a  horse  travel  10  miles  in  an  hour,  how 
many  times  10  miles  can  he  travel  in  5  twelfths  of  a 
day  ? 

108.  How  many  cents  will  1  quart  of  gin  cost,  if  1 
gill  cost  15  mills  ? 

109.  IIow  many  dollars  will  4  sixths  of  a  pound  of 
gold  cost,  if  1  pennyweight  cost  12  dimes  ?  / 

110.  How  many  eagles  will  25  fourths  of  a  gallon 
of  brandy  cost,  at  1  half  dime  a  gill  ?  / 

- «-<>--•—*>- - 

LESSON  II. 

1.  If  1  third  of  an  orange  cost  2  cents,  what  will  1 
orange  cost  ? 

Solution. — Tf  1  third  of  an  orange  cost  2  cents  ;  3  thirds,  or 
1  orange,  will  cost  3  times  2  cents,  which  are  6  cents. 


FRACTIONS. 


63 


2.  If  1  half  of  a  pound  of  raisins  cost  8  cents,  what 
will  1  pound  cost  ? 

3.  Bought  1  third  of  a  barrel  of  sugar  for  $3  ;  how 
much  will  2  thirds  of  a  barrel  cost,  at  the  same  rate  ? 

4.  If  1  third  of  a  pound  of  pork  cost  5  cents,  how 
much  will  2  pounds  cost? 

5.  2  is  1  third  of  what  number  ? 

Solution. — Tf  1  third  of  some  number  is  2,  3  thirds,  which  is 
that  number,  are  3  times  2,  or  G. 

6.  5  is  1  half  of  what  number  ? 

7.  It  1  fourth  ot  a  lemon  cost  2  cents,  what  will  1 
cost  ? 

b.  It  1  fourth  of  a  melon  cost  5  cents,  what  will  1 
cost  ? 

9.  3  is  1  fourth  of  what  number? 

10.  7  is  1  third  of  what  number? 

11.  12  is  1  fifth  of  what  number? 

12.  7  is  a  fourth  of  what  number? 

What  will  4  filths  of  a  pound  of  cinnamon  cost, 
if  1  fifth  of  a  pound  cost  5  cents  ? 

14.  If  1  fifth  of  a  yard  of  cloth  cost  $2,  what  will 
a  yard  cost  ? 

15.  It  1  sixth  of  a  gallon  of  vinegar  cost  2  cents, 
what  will  1  gallon  cost  ? 

16.  A  man,  being  asked  the  value  of  his  horse,  said, 
that  1  eighth  of  its  value  is  $12 ;  what  is  the  value 
of  the  horse  ? 

17.  A  man  gave  15  cents  for  his  lodging,  which 
was  1  seventh  as  much  as  his  breakfast  cost  him  ;  how 
much  did  he  give  for  his  breakfast  ? 

18.  Bought  1  eighth  ot  a  yard  of  cloth  for  4  dimes; 
what  will  a  yard  cost  at  that  rate  ? 

19.  If  1  tenth  of  a  yard  of  cloth  cost  47  cents,  how 
much  is  that  a  yard? 

20.  What  will  1  yard  of  cloth  cost,  if  1  ninth  of  a 
yard  cost  5  cents  ? 


64 


FRACTIONS. 


21.  What  will  1  bushel  of  corn  cost,  if  1  seventh  of 
a  bushel  cost  5  cents  ? 

22.  What  will  a  hogshead  of  molasses  cost,  if  1 
eighth  of  a  hogshead  cost  $3. 

23.  What  will  be  the  cost  of  2  cords  of  wood,  if  1 
eleventh  of  a  cord  cost  30  cents? 

24.  If  1  twelfth  of  the  distance  from  Albany  to 
Wilbraham  is  9  miles,  what  is  the  entire  distance  ? 

25.  9  is  1  tenth  of  what  number? 

26.  15  is  1  seventh  of  what  number? 

27.  16  is  1  fifth  of  what  number?' 

28.  12  is  1  fifth  of  6  times  what  number  ? 

29.  15  is  1  sixth  of  5  times  what  number? 

30.  18  is  1  fourth  of  6  times  what  number? 

31.  10  is  1  eighth  of  20  times  what  number? 

32.  15  is  1  seventh  of  5  times  what  number? 

33.  20  is  1  eighth  of  16  times  what  number? 

34.  30  is  1  third  of  C  times  what  number? 

35.  A  boy’s  hat  cost  $3,  which  was  1  fifth  of  the 
cost  of  his  coat.  The  cost  of  the  coat  is  required. 

36.  Mr.  B’s  saddle  cost  $9,  which  was  1  fortieth  of 
6  times  the  cost  of  his  horse.  The  cost  of  the  horse 
is  required. 

37.  Henry  gave  five  cents  for  a  piece  of  pie,  which 
was  1  twentieth  of  4  times  as  much  as  liis  breakfast 
cost  him  ;  what  was  the  cost  of  his  breakfast  ? 

38.  A  man,  being  asked  his  age,  answered,  that 
his  youngest  son’s  age,  which  was  12  years,  was  just 
1  twelfth  of  3  times  his  age.  Required  the  father  s 
age. 

"39.  Mrs.  B’s  shawl  cost  $9,  which  was  1  tenth  of 
3  times  the  cost  of  her  dress ;  what  was  the  cost  of 
her  dress  ? 

40.  John  said  to  James,  who  is  now  10  years  old, 
your  age  is  1  eighth  of  4  times  my  age.  How  old  is 
John  ? 


fractions. 


65 


LESSON  III. 


1.  If  2  thirds  of  a  melon  cost  4  cents,  what  will  1 
melon  cost  ? 

Solution. — If  2  thirds  of  a  melon  cost  4  cents,  1  third  will 
cost  1  half  of  4  cents,  which  is  2  cents,  and  3  thirds,  which  is  1 
melon,  will  cost  3  times  2  cents,  which  are  6  cents. 

2.  If  2  thirds  of  an  orange  cost  5  cents,  what  will  1 
orange  cost  ? 

O 

3.  If  3  fourths  of  a  pound  of  candies  cost  9  cents, 
what  will  1  pound  cost  ? 

4.  If  4  thirds  of  a  pound  of  spice  cost  16  cents, 
what  will  1  pound  cost  ? 

5.  If  3  fourths  of  a  pound  of  cinnamon  cost  12 
cents,  what  will  1  pound  cost  ? 

6.  If  $4  will  buy  2  fifths  of  a  barrel  of  fish,  what 
will  1  fifth  of  a  barrel  cost  ? 

7.  What  will  1  yard  of  cloth  cost,  if  4  sixths  of  a 
yard  cost  120  cents? 

8.  What  will  1  hogshead  of  molasses  cost,  if  5 
sevenths  of  a  hogshead  cost  $15. 

9.  8  is  2  thirds  of  what  number  ? 

Solution. — If  2  thirds  of  some  number  is  8,  1  third  of  that 
number  is  1  half  of  8,  which  is  4 ;  and,  3  thirds,  which  is  that 
number,  are  3  times  4,  which  are  12.  Therefore,  8  is  2  thirds 


of  12. 


Remark. — Representing  the  conditions  and  solution  of  ques¬ 
tions  by  symbols  will  aid  young  pupils  in  comprehending  the 
more  difficult  parts  of  arithmetical  analysis.  The  condition  and 
analysis  of  the  preceding  question  may  be  represented,  thus ; 


If 


=  |  of  some  number  =8, 


=  4  of  that  number  =4, 


■  =|}  which  is  that  number,  =12. 


66 


FRACTIONS. 


15.  12  is  2  thirds  of  what  number? 

16.  4  is  2  thirds  of  what  number? 

17.  10  is  2  sevenths  of  what  number? 

18.  9  is  3  fourths  of  what  number? 

19.  1 2  is  3  fourths  of  what  number? 

20.  12  is  6  elevenths  of  what  number  ? 

21.  14  is  7  eighths  of  what  number? 

22.  14  is  2  sevenths  of  what  number? 

23.  6  is  3  tenths  of  what  number? 

24.  9  is  3  sevenths  of  what  number? 

25.  15  is  5  sixths  of  what  number? 

26.  15  is  3  halves  of  what  number? 

27.  18  is  9  eighths  of  what  number? 

28.  20  is  5  thirteenths  of  what  number? 

29.  24  is  8  'fifths  of  what  number  ? 

30.  26  is  13  ninths  of  what  number  ? 

31.  2  thirds  of  12  is  2  fifths  of  what  number? 

32.  3  fourths  of  12  is  3  eighths  of  what  number? 

33.  3  fourths  of  8  is  2  seventh^  of  what  number  ? 

34.  3  fifths  of  25  is  5  fourths  of  what  number  ? 

35.  2  sevenths  ot  14  is  4  ninths  of  what  number? 

36.  4  sevenths  of  21  is  3  tenths  of  what  number? 

37.  2  thirds  of  15  is  5  fourths  of  what  number? 

38.  7  eighths  ot  48  is  3  halves  of  what  number? 

39.  8  ninths  of  36  is  4  fifths  of  what  number? 

40.  7  thirds  of  18  is  3  fifths  of  what  number? 

41.  A  watch  cost  $16,  and  3  halves  of  the  cost  of 
the  watch  is  8  thirds  of  the  cost  of  the  chain.  What 
was  the  cost  of  the  chain  ? 

42.  A  horse  was  sold  for  $96,  which  was  8  sevenths 
of  what  it  cost ;  what  was  the  cost  of  the  horse  ? 

43.  In  a  certain  school  there  are  36  ladies,  and  5 
fourths  ot  the  number  of  ladies  equals  3  fifths  of  the 
number  of  gentlemen.  How  many  gentlemen  were 
there  in  the  school  ? 

44.  Mary  is  14  years  old,  and  4  sevenths  of  her 
age  is  2  thirds  of  Ilezekiah’s  age  ;  what  is  his  age  ? 


i 


fractions. 


67 

45.  A  piece  of  clotli  containing  12  yards  was  sold 
for  $60,  which  was  5  fourths  ot  what  it  cost ;  how 
much  did  it  cost,  and  what  was  the  gain  on  each  yard  '. 

46.  A  has  48  geese,  and  3  fourths  ot  his  number  is 
equal  to  9  sevenths  of  B’s  number ;  how  many  geese 

llcLS  B  * 

47.  The  head  of  a  fish  is  12  inches  long,  and  3 
fourths  of  the  length  of  the  head  is  3  fifteenths  of  the 
length  of  the  body.  Required  the  length  ot  the  fish. 

48  A  farm  was  sold  for  $1200,  which  was  only  6 
sevenths  of  what  it  was  worth.  How  much  was  lost 

by  the  bargain  ?  .  ,  ,, 

49.  $48  is *3  fifths  of  the  cost  of  12  yards  of  cloth  ; 

for  what  must  it  be  sold  a  yard  to  gain  $16  on  the 

whole?  „ 

50.  A  man  gave  60  dollars  for  a  suit  of  clothes, 

which  was  1  fifth  of  his  yearly  income  ;  1  sixth  of  the 
remainder  he  spent  for  a  watch,  and  what  then  le- 
mained  was  4  fifths  of  his  brother’s  yearly  income. 
What  was  the  yearly  income  of  each  ? 

- -0  - - - 


LESSON  IV. 


2  thirds 

is 

written  thus 

2 

n  • 

O 

1  half 

tt 

it 

n 

1 

2* 

1  third 

tt 

it 

u 

1 

3  * 

1  fourth 

tt 

it 

u 

I 

4  * 

1  sixth 

it 

u 

u 

1 

6  * 

1  seventh 

it 

n 

u 

1 

7* 

3  fourths 

tt 

u 

it 

3 

4  * 

7  eighths 

tt 

tt 

it 

7 

8  * 

9  tenths 

tt 

tt 

u 

9 

1  0* 

5  sevenths 

it 

u 

u 

5 

7* 

2  fifths 

it 

tt 

it 

2 

5  * 

5  thirds 

it 

u 

it 

5 

3* 

&c. 

tt 

tt 

tt 

&c. 

08 


REDUCTION  OF  FRACTIONS. 


I 


Remark.— The  above  expressions  are  called  fractions.  The 
figure  above  the  short  horizontal  line  is  called  the  numerator,  and 
the  figure  belo  w  the  line  is  called  the  denominator.  For  example 

m  the  fi action  £,  the  3  is  the  numerator,  and  the  4  is  the  denom- 
inator. 

The  denominator  of  a  fraction  shows  into  how  many  equal 
parts  the  thing  is  divided  ;  and  the  numerator  shows  how  many 
^  of  these  parts  are  taken.  y 

1.  If  you  cut  an  orange  into  3  equal  parts,  what  is 
1  ot  these  parts  called  ? 

i  3 l01-n°a  !)0  cut  3nto  4  G€llml  pieces,  what  will 
1  ot  thnse  pieces  be  called  ?  2  ?  3  ?  42 

3  If  a  bushel  of  apples  be  divide^  into  6  equal 
parts,  what  will  1  of  these  parts  be  called  ?  3  ?  4  2  0  2 

4.  If  a  basket  of  peaches  be  divided  in  8  equal 
parts,  what  will  3  ot  these  parts  be  called  ?  5  ?  6  ?  7  ? 

5.  How  can  you  find  2  thirds  of  an  apple  ? 

6.  How  can  you  find  3  fourths  of  an  orange  & 

7.  In  |  how  many  times  1  ? 

Solution.— In  1  there  are  2  halves,  therefore  I  half  the  num¬ 
ber  of  halves  equals  the  number  of  ones.  1  half  of  4  is  2  • 
therefore,  f  equals  2.  1  4  13  z > 

In  f  how  many  times  1  ? 

In  f  how  many  times  1  ? 

In  -1/-  how  many  times  1  ? 

In  R2  how  many  times  1  2 

In  V  how  many  times  1  ? 

In  f  how  many  times  1  ? 

In  J32  how  many  times  1? 

In  f  how  many  times  1  ? 

In  -1/-  h°w  many  times  1  ? 

In  -1/  how  many  times  1  ? 

In  -1/  how  many  times  1  ? 

In  Y  how  many  times  1  ? 

In  |  how  many  times  1  ? 

In  -1/  how  many  times  1  ? 

In  -1/  how  many  times  1  ? 

In  y°-  how  many  times  1  ? 


8. 

9. 


REDUCTION  OF  FRACTIONS.  69 


24. 

In 

2  4 

4 

how 

many 

times 

1? 

25. 

In 

3  6 

4 

how 

many 

times 

1? 

26. 

In 

5 

5 

how 

many 

times 

1? 

27. 

In 

m 

5 

how 

many 

times 

1? 

28. 

In 

2  5 

5  ~ 

how 

many 

times 

1? 

29. 

In 

1  5 

5 

how 

many 

times 

1? 

30. 

In 

5  5 
.5 

how 

many 

times 

1? 

31. 

In 

6  0 

5 

how 

many 

times 

1? 

32. 

In 

1  8 

6 

how 

many 

times 

1? 

33. 

In 

3  6 

9 

how 

many 

times 

1  ? 

34. 

In 

4  8 

8 

how 

many 

times 

1? 

35. 

In 

5  0 

1  0 

how 

many 

times 

1? 

36. 

In 

4  5 
]  5 

how 

many 

times 

1? 

37. 

In 

7  2 

1  8 

how 

many 

times 

1? 

38. 

In 

1  0  0 

2  — 

how 

many 

times 

1? 

39. 

In 

5  6 

7' 

how 

many 

times 

1? 

40. 

In 

C  3 

9 

how 

many 

times 

1? 

41.  What  kind  of  a  fraction  is  it  called,  when  the 
numerator  is  less  than  the  denominator  ? 

42.  What  kind  of  a  fraction  is  it  called,  when  the 
denominator  is  greater  than  the  numerator  ? 

43.  When  is  the  value  of  a  fraction  greater  than  a 
unit  ? 

44.  When  the  denominator  is  less  than  the  numera¬ 
tor,  what  kind  of  a  fraction  is  it  called  ? 

45.  What  kind  of  a  fraction  is  it  called,  when  the 
numerator  is  larger  than  the  denominator  ? 

Remark. — This  is  called  reducing  fractions  to  whole  or  mixed 
numbers.  A  mixed  number  is  a  whole  number  with  a  fraction 
added  to  it.  Thus  3J  is  a  mixed  number. 

Whenever  the  numerator  is  less  than  the  denominator,  the  value 
is  less  than  a  unit,  and  the  expression  is  called  a  proper  fraction  ; 
■ — but  when  the  numerator  is  equal  to  or  greater  than  the  denom¬ 
inator  the  value  is  equal  to  or  greater  than  a  unit,  and  the  ex¬ 
pression  is  called  an  improper  fraction. 

46.  Reduce  |  to  a  mixed  number. 

47.  Reduce  f  to  a  mixed  number. 


70 


ADDITI 

ON 

0  F 

FEACTI 

ONS  . 

48. 

Reduce 

1  5 

~4 

to 

a 

mixed 

number. 

49. 

Reduce 

1  9 

3 

to 

a 

mixed 

number. 

50. 

Reduce 

2JI 

4 

to 

a 

mixed 

number. 

51. 

Reduce 

2_1 

5 

to 

a 

mixed 

number. 

52. 

Reduce 

5  Z 

_4 

to 

a 

mixed 

number. 

53. 

Reduce 

8  9 

1  2 

to 

a 

mixed 

number. 

54. 

Reduce 

9JL 

8 

to 

a 

mixed 

number. 

55. 

Reduce 

2  5 

3 

to 

a 

mixed 

number. 

56. 

Reduce 

3  7 
g 

to 

a 

mixed 

number. 

57. 

Reduce 

4' 7 

4 

to 

a 

mixed 

number. 

58. 

Reduce 

7  8 

7 

to 

a 

mixed 

number. 

59. 

Reduce 

3  7 

6 

to 

a 

mixed 

number. 

60. 

Reduce 

_3_4 

8 

to 

a 

mixed 

number. 

- - - 

LESSON  V. 

1.  James  had  £  of  an  apple,  and  John  gave  him  £ 
more  ;  how  many  had  he  then  ? 

2.  Mary  had  -f  of  an  orange,  and  her  father  gave 
her  £  of  an  orange  more  ;  how  many  had  she  then  ? 

3.  Robert  had  f  of  a  melon,  and  bought  f  of  an¬ 
other  ;  how  many  had  he  then  ? 

4.  Susan  had  £  of  a  pint  of  walnuts,  and  gave  £  of 
a  pint  to  her  sister;  how  much  had  she  left? 

5.  James  bought  -1/  of  a  pound  of  candies,  and  on 
his  way  home  ate  £  of  a  pound ;  how  much  had  he 
left  ? 

6.  John  gave  \  of  a  pound  of  raisins  to  James,  f  of 
a  pound  tollary,  and  kept  f  of  a  pound  himself;  how 
many  had  he  at  first  ? 

7.  Mortimer  gave  f  of  a  dollar  for  a  hat,  $lf  for  a 
vest,  and  had  $3|  remaining ;  how  much  had  he  at 
first? 

8.  Jane  had  5  pounds  of  cinnamon,  and  Harriet  had 
2£  pounds  ;  how  many  more  had  Jane  than  Harriet? 


ADDITION,  &C.,  OF  FRACTIONS.  7l 

9.  Henry  gave  §  of  a  dollar  for  his  breakfast,  f  of  a 
dollar  for  his  dinner,  and  |  of  a  dollar  for  his  supper ; 
how  much  did  his  day’s  board  cost  him  ? 

10.  -9-  -f-  f  are  how  many  ? 

11*  I  +  f  are  how  many  ? 

12.  f  +  f  are  how  many? 

13.  t9o+t8o  are  how  many? 

14.  f  +  f-  are  how  many  ? 

15.  */+  |  are  how  many? 

16.  +  f  are  how  many? 

17.  +  -+  are  how  many  ? 

18.  f  +  V1  are. how  many? 

19.  1  +  f  +  f  are  how  many? 

20.  £  +  f  +  £  are  how  many  ? 

21.  r7o  +  tV  +  r9o  arc  h° w  many  ? 

22.  f  +  £  +  j  are  how  many  ? 

23.  -f-  less  £  are  how  many  ninths? 

24.  y7-  less  y7-  are  how  many  ? 

25.  +- —  |  are  how  many  ? 

26.  y3- —  f  are  how  many? 

27.  -3y  —  |  are  how  many  ? 

28.  y  —  |  are  how  many  ? 

29.  -3g7- —  £  are  how  many? 

30.  +9- —  |  are  how  many  ? 

31.  -y. — j_p.  are  how  many? 

32.  -y- —  A  are  how  many? 

33.  || —  |Jare  how  many? 

34.  f  +  1  —  £  are  l10\v  many  ? 

35.  £  +  |  —  f  are  how  many  ? 

36.  £  + -Li —  |  are  how  many? 

37.  |£ — -f  ||  are  how  many? 

38.  |  of  60 — |  of  24  are  how  many? 

39.  1  of  40  —  |  of  10  are  how  many  ? 

40.  |  of  15+|  of  9— |  of  12  are  how  many? 


72  MULTIPLICATION  OF  FRACTIONS. 


LESSON  VI. 

1.  At  |  of  a  cent  a  piece,  what  will  2  apples  cost? 

Solution. — If  1  apple  cost  f  of  a  cent,  2  apples  will  cost 
twice  |  of  a  cent,  which  are  f  or  1|  cents. 

2.  At  |  of  a  cent  a  piece,  what  will  5  apples  cost? 

3.  At  |  of  a  dime  a  pound,  what  will  10  pounds  of 
candies  cost? 

4.  At  If  dimes  a  pound,  how  many  cents  will  8 
pounds  of  starch  cost? 

5.  At  |  of  a  cent  a  piece,  what  will  25  filberts  cost? 

6.  At  |  of  a  dime  a  piece,  how  many  cents  will  8 
chickens  cost  ? 

7.  At  |  of  a  dollar  a  yard,  what  will  15  yards  of 
linen  cost? 

8.  If  a  man  spend  f  of  a  dollar  a  day,  how  much, 
at  this  rate,  will  he  spend  in  23  days? 

9.  If  a  man  receive  f  of  an  eagle  in  a  week,  how 
many  dollars  will  he  receive  in  52  weeks  ? 

10.  If  1  pound  of  sugar  cost  If  dimes,  what  will  12 
pounds  cost? 

11.  At  5 1  cents  a  pound,  what  will  6  lbs.  of  beef 
cost  ? 

12.  At  9f  cents  a  pound,  what  will  8  lbs.  of  pork 
cost  ? 

13.  At  6f  cents  each,  what  will  12  lemons  cost? 

14.  At  7f  cents  each,  what  will  20  rabbits  cost? 

15.  At  12^  cents  a  dozen,  what  will  4  doz.  eggs 
cost  ? 

16.  At  Ilf  cents  a  pound,  what  will  6  pounds  of 
honey  cost? 

17.  At  $74  a  bal.  what  will  10  bals.  of  tobacco  cost  ? 

18.  At  $9f  a  barrel,  what  will  10  bals.  of  pork  cost? 

19.  What  will  6  boxes  of  raisins  cost,  at  $3f  a 
box? 


MULTIPLICATION  OP  FRACTIONS.  73 

20.  What  will  14  bushels  of  wheat  cost,  at  $1§  a 
bushel  ? 

21.  What  will  7  barrels  of  cider  cost,  at  f>3£  a 
barrel  ? 

22.  If  a  barrel  of  flour  cost  $4,  what  will  5  4  barrels 
cost  ? 

23.  5  times  4  and  f  of  4  are  how  many  ? 

24.  7  times  6  and  f  of  G  are  how  many  ? 

25.  9  times  7  and  f  of  7  are  how  many  ? 

26.  12  times  9  and  f  of  9  are  how  many  ? 

27.  5  times  10  and  f  of  10  are  how  many? 

28.  13  times  4  and  f  of  4  are  how  many  ? 

29.  8  times  7  and  4  of  7  are  how  many? 

30.  10  times  13  and  |4  of  13  are  how  many? 

31.7  times  20  and  f  of  20  are  how  many  ? 

32.  How  many  are  4  times  f  ? 

33.  How  many  are  4  times  2|  ? 

34.  How  many  are  3  times  4f  ? 

35.  How  many  are  5  times  3f,  +4  • 

36.  How  many  are  7  times  9|,  +|? 

37.  How  many  are  8  times  124,  —4  ? 

38.  How  many  are  9  times  lOf,  — f  ? 

39.  How  many  are  6  times  12|,  +24  ? 

40.  How  many  are  12  times  9|,  ;? 

- - - 

LESSON  VII. 

1.  If  you  give  to  6  persons,  each  |  of  a  dollar,  how 

many  dollars  will  it  take  ?  i 

2.  What  will  be  the  cost  of  4  yards  of  cloth,  at  j 

of  a  dollar  a  yard? 

3.  If  1  yard  of  cloth  cost  $1§,  what  will  10  yards 
cost? 

4.  How  many  oranges  will  it  require  to  give  to  each 
of  9  boys  14  oranges? 


7 


74  MULTIPLICATION  OF  FRACTIONS. 

5.  How  many  barrels  of  flour  does  that  man  give 
away,  who  gives  to  each  of  12  beggars  §  of  a  barrel. 

6.  Anthony  gave  to  each  of  his  7  companions  §  of 
a  pound  of  candies,  and  had  ^  of  a  pound  left;  how 
many  pounds  had  he  at  first  ? 

7.  Thornton  gave  to  each  of  9  beggars  f  of  a  dollar, 
and  had  $7  remaining  ;  how  much  had  he  at  first? 

8.  James  gave  y1^  of  an  orange  to  Jackson,  t5j  to 
Joseph,  and  ^  to  John  ;  what  part  of  an  orange  had 
he  remaining:  ? 

9.  Harmon  meeting  3  poor  women  and  5  poor  men, 
gave  to  each  woman  f  of  a  dollar,  and  to  each  man  J- 
of  a  dollar,  and  then  had  only  $4  remaining ;  how 
much  had  he  at  first  ? 

10.  How  many  quarts  of  chestnuts  must  that  boy 
have,  who  gives  to  each  of  20  persons  %  of  a  quart, 
and  has  7  quarts  remaining? 

11.  Mary,  after  giving  to  each  of  her  12  companions 
as  many  pinks  as  she  had  roses,  which  were  2,  had  no 
flowers  remaining  but  her  roses.  How  many  flowers 
had  she  at  first  ? 

12.  What  will  1  quart  of  vinegar  cost,  if  1  pint 
cost  |  of  a  cent? 

13.  If  1  gill  of  molasses  cost  |  of  a  cent,  what  will 
2  quarts  cost  ? 

14.  If  2  pints  of  beans  cost  4  cents,  what  will  1 
peck  cost? 

15.  If  3  pecks  of  buckwheat  cost  96  cents,  what 
will  1  pint  cost  ? 

16.  What  will  10  yards  of  silesia  cost,  if  1  yard 
cost  18|-  cents? 

17.  How  many  cents  will  4f  yards  of  silk  cost,  if  1 
yard  cost  6  dimes  ? 

18.  What  will  f  of  a  yard  of  muslin  cost,  if  1  yard 
cost  10  cents? 

19.  What  will  7  spools  of  thread  cost,  if  1  spool  cost 
7f  cents? 


MULTIPLICATION  OF  FRACTIONS.  75 

20.  What  will  8f  yards  of  silk  cord  cost,  at  6  cents 
a  yard  ? 

21.  If  1  yard  of  wadding  cost  5  cents,  what  will 
9  j  yards  cost  ? 

22.  What  will  6f  yards  of  muslin  cost,  if  1  yard 
cost  8  cents  ? 

23.  What  will  8|  pounds  of  veal  cost,  at  5  cents  a 
pound  ? 

24.  IIow  much  will  9£  barrels  of  cider  cost,  at  $4  a 
barrel  ? 

25.  What  will  12  hats  cost,  at  $3£  each  ? 

26.  AVhat  will  5£  yards  of  gingham  cost,  at  4  dimes 
a  yard  ? 

27.  What  will  be  the  cost  of  13  yards  of  bishop 
lawn,  at  $1T43  a  yard  ? 

28.  AYhat  will  be  the  cost  of  8  looking  glasses,  at 
$15|  a  piece  ? 

29.  What  amount  of  money  will  be  required  to 
purchase  30  pounds  of  rice,  at  6§  cents  a  pound  ? 

30.  AYhat  will  be  the  cost  of  23  pounds  of  crackers, 
at  8|-  cents  a  pound  ? 

31.  AYhat  will  9  barrels  of  fish  cost,  at  $12f  a  barrel  ? 

32.  If  1  grain  of  gold  cost  9L  dimes,  what  will  1 
pennyweight  cost? 

33.  If  1  gold  pen  cost  $2f  how  much  will  0  cost? 

34.  IIow  many  pounds  of  meat,  at  5  cents  a  pound, 
can  you  buy  for  $3f  ? 

35.  AYhat  will  be  the  cost  of  3  quarts  of  nuts,  at  64 
cents  a  peck? 

36.  If  a  coachman  charge  5^-  cents  a  mile,  how 
much  must  that  man  pay  who  rides  12  miles? 

37.  How  many  dollars,  dimes,  and  cents  will  12 
yards  ot  cloth  cost,  at  62  cents  a  yard? 

38.  How  many  dollars  and  cents  will  4  pecks  of 
grass  seed  cost,  if  1  pint  cost  5  cents  ? 

39.  How  much  will  13  yards  of  shalloon  cost,  atl3f 
cents  a  yard? 


76  MULTIPLICATION  OF  FRACTIONS. 

40.  How  many  cents  will  16  bushels  of  potatoes 
cost,  at  2 f  dimes  a  bushel  ? 

r 

- - 

r 

c 

1  LESSON  VIII. 

‘  IfyW"  Remark;. — A  fraction  may  be  multiplied,  by  multiplying 

the  numerator  (as  you  have  already  observed),  or  by  dividing 
*  the  denominator. 

‘  1.  How  many  are  5  times  ^  ? 

Solution. — 5  times  t7q  are  -f-%,  or  3f. 

:  Remark. — In  accordance  with  the  above  remark  we  have 

Solution. — 5  times  T\  are  f,  or  3  A 

2.  How  many  are  3  times  ? 

3.  How  many  are  9  times  o6j  ? 

4.  How  many  are  5  times  f  f  ? 

5.  How  many  are  6  times  f  f  ? 

6.  How  many  are  9  times  T4¥  ? 

7.  How  many  are  9  times  if  ? 

8.  How  many  are  7  times  f  f  ? 

9.  8  times  if  are  how  many  ? 

10.  11  times  if  are  how  many? 

11.  13  times  if  are  how  many? 

12.  2  times  f-  are  how  many  ? 

13.  5  times  if  are  how  many? 

14.  6  times  if  are  how  many? 

15.  7  times  f  £  are  how  many  ? 

16.  12  times  if  are  how  many? 

17.  How  many  times  5  are  8  times  if  ? 

18.  How  many  times  12  are  9  times  if  ? 

19.  How  many  times  8  are  11  times  f  f  ? 

20.  How  many  times  100  are  25  times  -\0/? 

21.  How  many  times  20  are  35  times  -W1  ? 

22.  5  times  is  4  times  Mary’s  age ;  what  is  her 

age 


MULTIPLICATION  &C.,  OF  FRACTIONS.  77 

23.  13  times  J36g0-  equals  £  of  the  number  of  dollars 
a  certain  wagon  cost.  Required  the  cost  of  the 
wagon. 

24.  25  times  equals  °f  the  number  of  men 
Gen.  Santa  Anna  had  at  the  battle  of  Buena  Vista. 
How  many  men  had  he  ? 

25.  6  times  2T\°-  is  of  the  number  of  men  he  had 
wounded.  How  many  men  were  wounded  ? 

26.  7  times  5T\9  is  £  of  the  number  of  men  he  had 
killed.  How  many  were  killed  ? 

27.  4  times  A|-®-  is  of  the  number  of  men  Gen. 
Taylor  had.  How  many  had  he  ? 

28.  9  times  A1  is  y  of  the  number  of  men  he  had 
killed.  How*  many  were  killed  ? 

29.  8  times  is  r.  0f  jlow  many  times  3  ? 

30.  4  times  f  a  is  i  of  how  many  times  5  ? 

31.  A  laborer  worked  12  months,  at  the  rate  of  $10f 
a  month ;  how  much  did  his  year’s  wages  amount  to  ? 

32.  It  2  quarts  of  wine  cost  48  cents,  what  will  1 
gill  cost? 

33.  How  much  ought  I  to  pay  for  3  oranges,  at  #  of 
a  cent  a  piece  ? 

34.  If  a  certain  piece  of  work  can  be  performed  in 
96  hours,  how  many  days  will  be  required  to  perform 
it  by  working  6  hours  a  day  ? 

35.  It  1  man  can  dig  a  ditch  in  15  days,  how  long 
will  it  take  5  men  to  dig  it  ? 

36..  It  a  certain  quantity  of  provision  serve  a  family 
of  4  persons  16  days,  how  long  would  it  last  a  family 
of  8  persons  ? 

37.  If  8  men  can  perform  a  certain  piece  of  work 
in  56  days,  in  how  many  days  can  112  men  do  the 
same  ? 

38.  If  3  men  can  plow  18  acres  in  6  days,  in  how 
many  days  could  9  men  do  the  same? 

39.  4  men  can  mow  a  certain  field  in  6^-  days,  in 
how  many  days  can  5  men  perform  the  same  work  ? 

7* 


78  MULTIPLICATION  &C.,  OF  FRACTIONS. 

40.  A  man  bought  6  barrels  of  cider,  at  $3§  a 
barrel ;  how  many  boxes  of  butter,  at  $4  a  box,  will  it 
take  to  pay  for  it  ? 

41.  A  merchant  bought  6  yards  of  cloth  and  sold 
it  for  $20  which  was  Jg°-  of  what  it  cost ;  what  did  it 
cost  a  yard  ? 

42.  Bought  36  yards  of  cloth,  and  sold  f  of  it  for 
$25,  which  was  f-  of  what  it  cost ;  how  much  would 
I  have  gained  by  selling  the  whole  at  the  same  rate  ? 

43.  7  men  in  -f  of  a  day  can  earn  $10,  how  long 
would  it  take  1  man  to  earn  the  same  ? 

44.  James  is  3|  years  of  age,  which  is  i  of  the  age 
of  Henry ;  and  Henry  is  9  times  as  old  as  George. 
What  is  the  age  of  Henry,  and  of  George  respectively? 

45.  i  of  36  is  3  times  i  of  what  number  ? 

46.  £  of  32  is  |  of  three  times  what  number  l 

47.  §-  of  60  is  §  of  twice  what  number? 

48.  |  of  40  is  -f  of  as  many  dollars  as  Mr.  B’s  horse 

cost ;  what  was  the  cost  of  his  horse  ? 

49.  A  person,  being  asked  his  age,  said,  that  £  of  80 
was  |  of  ten  times  his  age.  What  was  his  age  ? 

50.  Morgan  is  20  years  old,  and  f  of  his  age  is 
of  the  age  of  his  brother.  What  was  his  brother’s 
age  ? 

- ♦♦♦•»«.» - 

LESSON  IX. 

1.  How  many  thirds  are  there  in  3  ? 

Solution. — In  1  there  are  3  thirds,  and  in  3  there  are  3  times 
3  thirds,  which  are  f . 

The  following  solution  is  preferred  to  the  above. 

Solution. — In  1  there  are  3  thirds,  therefore,  3  times  the 
number  of  whole  ones,  equal  the  number  of  thirds.  3  times  3 
are  9.  Therefore,  in  3  there  are  f . 

2.  How  many  fourths  are  there  in  3  ? 

3.  How  many  halves  are  there  in  6  ? 


DIVISION  OF  F  Ii  A  C  T  I  O  N  S  . 


*79 


4.  How  many  fifths  are  there  in  4  ?  in  5  ? 

5.  IIow  many  fifths  are  there  in  7  ?  in  8  ? 

6.  How  many  sixths  are  there  in  4  ?  in  3  ?  in  5  ? 

7.  How  many  sevenths  are  there  in  2  ?  in  4  ?  in  6  ? 

8.  How  many  eighths  are  there  in  7  ?  in  4?  in  5  ? 

9.  How  many  fifteenths  are  there  in  2?  in  3  ?  in  6  ? 

10.  Ilcrw  many  tenths  are  there  in  4  ?  in  6?  in  7 

11.  How  many  fourths  are  there  in  3  and  f-  ? 

12.  How  many  thirds  are  there  in  4  and  ±  ? 

13.  How  many  thirds  are  there  in  3  and  f  ? 

14.  How  many  halves  arc  there  in  8  and  -i  ? 

15.  Reduce  6f  to  an  improper  fraction. 

16.  Reduce  9f  to  an  improper  fraction. 

17.  Reduce  7f  to  an  improper  fraction. 

18.  Reduce  5f  to  an  improper  fraction. 

19.  Reduce  4f  to  an  improper  fraction. 

20.  Among  how  many  men,  can  5f  bushels  of 
wheat  be  distributed,  provided  each  receives  f  of  a 
bushel  ? 

21.  Among  how  many  boys,  can  7f  oranges  be 
divided,  provided  each  receives  f  of  an  orange? 

22.  8  and  f-  are  how  many  times  f  ? 

Solution.— 8  and  §  equal  7¥4.  £  is  contained  in  74  31  times. 

23.  9f  are  how  many  times  f  ? 

24.  9f  are  how  many  times  £  ? 

25.  7f  are  how  many  times  £? 

26.  12f  are  how  many  times  f  ? 

27.  7 4  are  how  many  times  f  ? 

28.  7f  are  how  many  times  f  ? 

29.  4£  are  how  many  times  f  ? 

30.  10J-  are  how  many  times  f  ? 

31.  8£  are  how  many  times  £  ? 

32.  12f  are  how  many  times  f  ? 

33.  4  times  3£  are  how  many  times  f  ? 

34.  9  times  If  are  how  many  times  £  ? 

35.  5  times  6f  are  how  many  times  f  ? 


80 


DIVISION  OF  FK  ACTIONS. 


36.  8  times  8|  are  how  many  times  f  ? 

37.  6  times  2|  are  liow  many  times  -2  ? 

38.  A  boy  distributed  apples  equally  among  his 
companions,  giving  to  each  4  of  an  apple ;  how  many 
companions  had  he  ? 

39.  Homer  distributed  $12f  equally  among  some 
poor  women,  giving  to  each  ;  how  many  women 
were  there  ? 

40.  Mary  gave  f  of  a  pie  to  each  of  her  9  visitors ; 
how  many  pies  did  it  take  ? 

41.  Bought  8  yards  of  cloth,  at  $5§  a  yard;  how 
many  yards  of  silk,  worth  $1}  a  yard  will  it  take  to 
pay  for  it  ? 

42.  Bought  9  yards  of  cloth,  worth  a  yard,  and 
paid  for  it  with  raisins,  at  a  box  ;  how  many  boxes 
did  it  take  ? 

43.  How  many  bushels  of  turnips,  at  $f  a  bushel, 
can  be  bought  for  8  bushels  of  apples,  at  $2  a  bushel  ? 

44.  How  many  apples,  at  £  of  a  cent  each,  can  be 
bought  for  6  oranges,  at  2£  cents  a  piece  ? 

45.  How  many  yards  of  cloth,  at  $4  a  yard,  can  be 
bought  for  10  boxes  of  butter,  at  $ 5 -2  a  box  ? 

46.  How  many  geese,  at  each,  can  be  bought 
for  14  ducks,  at  a  piece? 

47.  How  many  boxes  of  cheese,  worth  $2£  a  box, 
may  be  had  for  17  boxes  of  butter,  at  $1-2  a  box? 

48.  How  many  barrels  of  flour,  worth  $5|  a  barrel, 
may  be  had  for  17  bunches  of  cotton,  at  $14.  a  bunch  ? 

49.  How  many  sheep,  at  $12-  a  head,  may  be  had 
for  8  calves,  at  $3|  each  ? 

50.  How  many  quarts  of  alcohol,  at  §  of  a  cent  a 
pint,  may  be  had  for  12  quarts  of  molasses,  at  42  cents 
a  quart? 

51.  Mary  and  Jane  together  picked  5  times 
quarts  of  strawberries  and  shared  them  equally  with 
their  companions;  how  many  companions  had  each, 
provided  each  received  12  quarts? 


DIVISION  OF  FRACTIONS. 


81 


lesson  X. 


-LEHSONS  NINTH  AND  TENTH  COMBINED. 

,h  faction  may  be  divided,  by  multiplying 

the  denominator ,  or  by  dividing  the  numerator. 

1.  If  2  yards  of  cloth  cost  $f,  what  will  1  yard 
cost  ?  J 


,  SOI'OTION.— If  2  yards  cosi  4  of  a  dollar,  1  yard  will  cost  i  c 
s  of  a  dollar,  which  is  f  of  a  dollar.  2 

2.  If  3  apples  cost  -f  of  a  cent,  what  will  1  ar>pl< 

cost  ?  1  r 

3.  It  2  oranges  cost  -f  of  a  cent,  what  will  1  oranm 

cost  ?  & 

4  If  3  yards  of  cord  cost  -j-f  of  a  cent,  what  will  ] 
yard  cost  ? 

5  If  2  pounds  of  sugar  cost  8§,  (or  y  cents,)  whal 

will  1  pound  cost  ?  J 

6  If  2  pine-apples  cost  14|  cents,  what  will  1  pine¬ 
apple  cost  ?  r 

1.  If  f  of  a  melon  is  worth  2  oranges,  how  much  is 
1  orange  worth  ? 

8.  If  3  apples  are  worth  2f  quinces,  what  is  1  apple 
worth  ?  11 


9.  How  many  times  7  are  \\  2 

10.  How  many  times  13  are  7|  ? 

11.  How  many  times  7  are  9^-? 

12.  How  many  times  21  are  16^  2 

13.  How  many  times  8  are  33|  ? 

14.  How  many  times  7  are  104? 

15.  How  many  times  11  are  40^  ? 

16.  How  many  times  18  are  14f  ? 

17.  How  many  times  3  are  4j  ? 

18.  How  many  times  0  are  7f  ? 

19.  How  many  times  6  are  6f  ? 

20.  How  many  times  15  are  33^  ? 


82 


DIVISION  OF  FRACTIONS. 


21.  If  9  oranges  are  worth  8^,  liow  many  cents  is 
1  orange  worth  ? 

22.  If  4  boxes  of  figs  cost  |  of  an  eagle,  how  many 
dollars  will  1  box  cost  ? 

23.  If  7  pounds  of  cheese  cost  $T\,  how  many  cents 
will  1  pound  cost  ? 

24.  If  3  cates  cost  t9<j  of  a  dime,  how  many  cents 
will  1  cate  cost  ? 

25.  If  4  pounds  of  chocolate  cost  4|  dimes,  how 
many  cents  is  that  a  pound  ? 

26.  What  will  1  portfolio  cost,  if  3  cost  T95-  of  an 
eagle  ? 

27.  If  8  quarts  of  alcohol  cost  32  dimes,  how  many 
cents  will  2  gills  cost  ? 

28.  What  will  1  pound  of  sugar  cost,  if  4  pounds 
.cost  - 1 S9-  cents  ? 

29.  If  6  pounds  of  cheese  cost  31 1  cents,  what  will 
1  pound  cost  ? 

30.  If  12  eggs  cost  9f  cents,  what  will  be  the  cost 
of  1  egg  ? 

31.  If  7  yards  of  cloth  cost  $241,  what  will  1  yard 
cost  ? 

32.  If  5  silk  shawls  cost  $274,  how  much  is  that 
apiece  ? 

33.  If  9  pair  of  boots  cost  $32|,  how  much  is  that 
a  pair  ? 

34.  If  9  oranges  are  worth  30|  walnuts,  how  many 
walnuts  is  1  orange  worth  ? 

35.  A  boy  gave  8  apples  for  18|  marbles,  how  many 
marbles  did  he  get  for  1  apple  ? 

36.  A  boy  gave  7  cents  for  l7i  crackers;  liow 
many  did  he  get  for  1  cent  ? 

37.  Mary  gave  10  pins  for  23^  chestnuts  ;  how  many 
did  she  get  for  1  pin  ? 

38.  If  3  yards  of  broadcloth  are  worth  18|  yards 
of  muslin,  how  many  yards  of  muslin  may  be  had  for 
1  yard  of  broadcloth  ? 


DIVISION  OF  FRACTIONS. 


83 


39.  If  John  can  walk  13  miles  while  Josiah  is  walk- 
32^  miles,  how  far  can  Josiah  walk  while  John  is 
walking  1  mile? 

40.  If  2  chestnuts  are  worth  T27  of  a  cent,  and  20 
chestnuts  are  worth  f  of  a  lemon,  how  many  cents  is 
1  lemon  worth  ? 

41.  If  2  oranges  cost  §  of  a  cent,  what  will  1  orange 
cost? 

Solution. — If  2  oranges  cost  f  of  a  cent,  1  orange  will  cost 
\  of  §  of  a  cent,  which  is  f  of  a  cent. 

42.  If  3  yards  of  linen  cost  $lf,  what  will  1  yard 
cost  ? 

43.  If  7  yards  of  tape  cost  13|  cents,  what  will  1 
yard  cost? 

44.  If  2  pints  of  molasses  cost  If  dimes,  how  many 
cents  will  1  gallon  cost? 

45.  How  many  times  8  are  6f  ? 

46.  How  many  times  6  are  5|? 

47.  How  many  times  4  are  4£  ? 

48.  How  many  times  2  are  13f  ? 

49.  How  many  times  7  are. 74? 

50.  How  many  times  8  are  9  times  f-f- 2 

51.  How  many  times  3  are  6  times  Iff? 

Solution. — Iff  equals  f  |.  6  times  are  qj.  3  is  con¬ 

tained  in  -25-  -2J1,  or  3g  times. 

52.  How  many  times  9  are  10  times  213zr? 

53.  How  many  times  7  are  5  times  3^? 

54.  How  many  times  5  are  15  times  3/^? 

55.  How  many  times  7  are  15  times  If  f  ? 

56.  How  many  times  5  are  3  times  2|  ? 

57.  How  many  times  six  are  4  times  5f  ? 

58.  If  If  yards  of  cloth  are  worth  $2f,  what  is  1 
yard  worth  ? 

59.  If  6f  bunches  of  grapes  are  worth  40  cents, 
how  many  cents  is  1  bunch  worth  ? 

60.  If  3f  baskets  of  peaches  are  worth  $5f,  what  is 
1  basket  of  peaches  worth  ? 


84 


FRACTIONS. 


LESSON  XI. 

I.  What  is  \  of  2  2 

Solution.— |  of  1  is  $ ;  and,  if  £  of  1  is  £,  £  of  2  is  twice  £, 
which  are  f .  Therefore  £  of  2  is  $-  of  1. 

2.  What  is  i  of  4  2  of  8  2 

3.  What  is  j-  of  2  2  3  2  5  2  7  2  9  ? 

4.  What  is  i  of  3?  5?  7?  9?  11? 

5.  What  is  £  of  2  2  3  ?  4  2  7  ?  8  2 

6.  What  is  J-  of  2  2  3  2  5  2  7  2  9  ? 

7.  What  is  -I  of  2  2  3  2  5  2  4  ?  6  ?  9  2  1 1  2 

8.  What  is  |  of  2?  42  3?  5?  6?  7?  9? 

9.  What  is  i  of  2  2  4?  7?  G?  3?  122  11? 

10.  What  is  XV  of  7  2  2  2  4  2  6  ?  9  2  14  2  15  2 

II.  If  2  apples  cost  3  cents,  what  will  1  apple  cost? 

Solution. — If  2  apples  cost  3  cents,  1  apple  will  cost  ^  of  3 
cents,  which  is  §,  or  H  cents. 

12.  If  2  apples  cost  5  cents,  what  will  1  apple  cost? 

13.  If  3  pens  cost  8  cents,  what  will  1  pen  cost? 

14.  If  3  yards  of  tape  cost  14  cents,  what  will  1 
yard  cost  2 

15.  If  5  barrels  of  flour  cost  $21,  what  will  1  bar¬ 
rel  cost  2 

16.  If  7  pecks  of  dried  apples  cost  23  dimes,  what 
will  1  peck  cost? 

17.  If  4  chickens  cost  9  dimes,  what  will  1  chicken 
cost  2 

18.  What  will  1  pound  of  tamarinds  cost,  if  6 
pounds  cost  27  dimes  2 

19.  What  will  1  barrel  of  flour  cost,  if  3  barrels 
cost  $25  2 

20.  If  you  divide  7  bushels  of /wheat,  equally, 
among  5  persons,  how  much  will  each  receive  2 

21.  Joshua  had  13  marbles,  and  Lewis  had  \  as 
many  -f  i  of  a  marble ;  how  many  had  he  2 


FRACTIONS. 


85 


22.  A  man  divided  3  barrels  of  flour  equally  among 
11  families  ;  what  part  of  a  barrel  did  each  receive  ? 

23.  A  farmer  divided  5  bushels  of  rye,  equally, 
among  7  of  his  poor  neighbors ;  what  part  of  a  bushel 
did  he  give  to  each  ? 

24.  Calvin  had  4  pints  of  nuts,  and  shared  them, 
equally,  with  0  of  his  companions ;  how  much  did 
each  receive  ? 

25.  Margaret,  having  7  quarts  of  raspberries,  shared 
them,  equally,  with  8  of  her  playmates ;  what  part  of 
a  quart  did  each  receive  ? 

26.  What  will  1  pound  of  prunes  cost,  if  5  pounds 
cost  48  dimes  ? 

27.  What  will  2  boxes  of  figs  cost,  if  7  boxes  cost 
29  dimes  ? 

28.  What  will  4  quarts  of  strawberries  cost,  if  9 
quarts  cost  7  dimes  ? 

29.  What  is  t  of  2  ? 

30.  If  T  of  2  is  f,  what  is  §  of  2  ? 

31.  What  is  f  of  5  ? 

Solution. — £  of  5  is  and  §  are  2  times  f,  which  are  y°, 
or  3  r. 

32.  What  is  £  of  3  ?  of  5  ?  6  ?  7  ?  9  ?  11  ? 

33.  What  is  |  of  2?  of  3  ?  4  ?  9?  11  ?  13? 

34.  What  is  £  of  2  ?  of  3  ?  5  ?  7  ?  9  ?  15  ? 

35.  What  is  £  of  3  ?  of  5  ?  8  ?  9  ?  12  ?  20  ? 

36.  What  is  £  of  4?  of  6  ?  8?  12?  11?  17? 

37.  What  is  |  of  3  ?  of  5  ?  6  ?  9  ?  10  ?  15  ? 

38.  What  is  T3T  of  2  ?  of  4  ?  5  ?  6  ?  10  ?  12  ? 

39.  What  is  T52  of  2  ?  of  4  ?  3  ?  9  ?  15  ?  21  ? 

40.  What  is  T\  of  7  ?  of  8  ?  9  ?  12  ?  15  ?  25  ? 

41.  IIow  many  cents  will  §  of  a  pound  of  candies 
cost,  if  1  pound  cost  2  dimes  ? 

42.  What  will  be  the  cost  of  f  of  a  box  of  raisins, 
if  1  box  cost  $3  ? 

43.  What  will  be  the  cost  of  f  of  a  yard  of  cloth, 
at  7  dimes  a  yard  ? 


8 


86  SIMPLE  PROPORTION. 

Pb 

44.  If  a  ton  of  hay  cost  $10,  what  will  2|  tons 
cost  ? 

45.  Jeremiah  is  91  years  old,  and  f  of  his  age  equals 
the  age  of  his  oldest  son  ;  how  old  is  he? 

46.  Bought  24  yards  of  cloth  for  $48 ;  but,  being 
damaged  1  sold  f  of  it,  at  $lf  a  yard,  and  the  re¬ 
mainder  for  what  it  cost.  How  much  did  I  lose  ? 

47.  Bought  14  yards  of  cloth  ?  and  sold  f  of  it,  at 
$2  a  yard,  which  amounted  to  $2  less  than  the  whole 
piece  cost.  What  did  it  cost  a  yard? 

48.  A  horse  was  sold  for  $97,  which  was  If  times 
as  much  as  it  cost.  What  did  the  horse  cost? 

49.  If  9  yards  of  cloth  cost  $17,  what  will  3  yards 

cost?  -  f  ' 

50.  If  7  jTards  of  cloth  cost  $25,  what  will  9  yards 
cost  ? 

51.  What  will  2  pounds  of  opium  cost,  if  5  pounds 
cost  $42  ? 

52.  If  5  pounds  of  indigo  cost  $32,  what  will  2 
pounds  cost? 

53.  A  wagon  was  sold  for  $90,  which  was  f-  of  what 
it  cost.  How  much  did  it  cost? 

54.  Two  men  started  from  the  same  place,  and 
traveled  the  same  way  ;  one  at  the  rate  of  92  miles  in 
10  hours  ;  the  other  at  the  rate  of  lj1^  miles  in  f  of  an 
hour;  how  far  apart  will  they  be  in  2  hours? 

55.  By  a  pipe  4f  gallons  of  water  run  into  a  cistern 
in  1  minute ;  how  much  did  the  vessel  hold  provided 
it  was  filled  in  9  minutes  ? 

56.  If  7  men  can  perform  a  certain  piece  of  work 
in  13f  days;  how  long  would  it  take  4  men  to  do  the 
same  ? 

* 

57.  If  5  persons  consume  a  barrel  of  flour  in  9 
weeks,  what  part  of  a  barrel  would  they  consume  in  5 

weeks  ? 

58.  If  a  man  earn  $f  in  a  day,  and  a  boy  $f,  how 
much  will  they  both  earn  in  6  days  ? 


87 


iff  $  y 

it 


SIMPLE  PROPORTION. 

59.  Antliony  spent  4  of  all  liis  money,  and  the  re^ 
mainder  he  gave  tor  8  yards  of  cloth,  at  $2y  a  }aid  , 

how  much  had  lie  at  first  ? 

60.  From  a  piece  of  cloth  a  tailor  cut  5  garments, 
each  containing  3y  yards ;  and  there  remained  2j 
yards ;  how  many  yards  did  the  piece  contain  ? 

^  61. 1  What  will  9  pounds  of  rice  cost,  if  7  pounds 

cost  43  cents?  .  .  . 

62.  An  individual,  after  spending  y-f  ot  all  his 
money,  had  only  $40  remaining ;  how  much  had  he 

first  ? 

63.  An  old  lady  bought  30  eggs,  at  the  rate  of  2 

for  5  cents;  what  did  they  cost?  ^ 

64.  How  much  will  13  pounds  of  coftee  cost,  if  26 

pounds  cost  $7  ?  . 

65.  What  will  7  gallons  of  molasses  cost,  it  6  pints 

cost  27  cents  ? 

66.  If  5  lamps  cost  $7y  what  will  7  lamps  cost  ? 

67.  If  5  horses  can,  in  4f  days,  consume  20  bushels 
of  oats,  in  how  many  days  can  11  horses  consume  the 

same?  *  -  .  .  ,» 

68.  If  15  gold  pens  cost  $20,  what  will  5  ot  them  cost  i 

69.  If  -  of  an  acre  of  land  be  worth  $14,  what  are 
10  acres  worth  ? 

70.  $25  is  4  of  the  cost  of  B’s  watch;  what  was 

the  cost  of  his  watch  ?  •  . 

71.  Mortimer’s  hat  cost  $5,  and  f  of  the  cost  ot  his 
hat  is  TV  of  the  cost  of  his  coat ;  what  was  the  cost  of 

his  coat?  - 

72.  If  a  man  in  T4y  of  a  day  walk  8  miles,  how  tar 

can  he  walk  in  5  days  ? 

73.  From  a  piece  of  cloth  containing  20  E.  Ir.,  a 
tailor  cut  8  suits  of  clothes,  each  containing  2f  yards ; 
how  many  yards  remained  ? 

74.  If  a  man  can  cut  1  cord  of  wood  in  5  hours, 
how  many  cords  can  he  cut  in  4  days,  by  working  1 2 
hours  a  day  ? 


88 


W 


l  y  .  •  _ t  > 

y  \  r  /cf 


7*  / 

SIMPLE  PEOPOETION, 


75.  A  man  bought  7  sheep,  at  the  rate  of  9  for 
$5^4  what  did  they  cost  him  ? 

76.  A  boy  bought  13  oranges, — giving  9  apples  for 

3  oranges  ;  how  many  apples  did  his  oranges  cost  him  ?  ] 

77.  If  25  cents  buy  7  lemons,  how  many  cents  will 

9  lemons  cost?  ..  / 

78.  |  of  45  equals  £  as  many  dollars  as  Andrew 
has  ;  how  many  dollars  has  he?  £  c, 

79.  $30-|  is  y  of  all  the  money  A  had  ;  how  much 
money  had  he  ? 

80.  What  will  3  pecks  of  flax-seed  cost,  if  3  pints 
cost  3  dimes  ? 

81.  What  will  1  quart  of  clover-seed  cost,  if  2  pecks 
cost  $3  and  2  dimes. 

82.  4i  times  7  is  i  of  what  number  ? 

83.  §  of  36  is  i  of  what  number? 

84.  i  of  36  is  -f-  times  what  number  ?  :  * 

85.  |  of  A’s  age  is  3  times  B’s  age ;  and  B  is  9 
years  old.  What  is  A’s  age  ? 

86.  An  individual,  being  asked  the  number  of  hours 
he  labored  each  day,  answered,  li  times  the  number 
ot  hours  in  a  day  is  3  times  as  many  hours  as  I  labor. 
How  many  hours  did  he  labor  each  day  ? 

87.  |  of  15  is  -i  of  what  number? 

88.  i  of  21  is  11  times  what  number? 

89.  |  of  24  is  If  times  what  number? 

90.  Wright  is  16  years  old,  and  1£  times  his  age  is 
If  times  Charles’s  age.  How  old  is  Charles? 


»■ 


LESSON  XII. 


LESSONS  EIGHTH,  NINTH,  AND  TENTH  COMBINED. 

S1W°  Remark. — Pupils  must  exercise  their  own  judgment  in 
employing  the  shortest  of  the  methods  given  in  lessons  eighth  and 
tenth  for  multiplying  and  dividing. 

1.  If  3  barrels  of  flour  cost  $13£,  what  will  6  cost? 

Solution. — $13£  equals  If  3  barrels  of  flour  cost  $-53-, 


SIMPLE  PROPORTION. 


89 


Tr 


6  barrels,  which  are  2  times  3  barrels,  will  cost  2  times 
which  are  $-525-,  or  $27|. 

2.  If  5  pounds  of  opium  cost  $27^,  what  will  20 

pounds  cost 2  ;7  >  -  \  -  */ *.•: ► 

3.  If  3  pounds  of  sugar  cost  l7f  cents,  wliat  will 

24  pounds  cost  ? 

4.  How  many  apples  will  pay  for  9  oranges,  if  8 
apples  are  worth  12f  oranges  ? 

Solution.— 12 1  oranges  equal  -64-  oranges.  If  -r/-  oranges  are 
worth  8/ apples  £  of  an  orange  is  worth  of  8  apples,  which  is 
^  or  l  of  an  apple-;  and  J,  which  is  1  orange,  are  worth  5 
times  g,  or  |  of  an  apple,  and  9  oranges  are  worth  9  times 
which  are  -48-,  or  5|  applet. 

Remark. — In  solving  questions  in  Proportion  never  seek  the 
value  of  a  unit  of  the  denomination  like  the  answer. 


5.  How  many  chestnuts  will  pay  for  9  walnuts,  if 
7  chestnuts  are  worth  lOf  walnuts? 

6.  If  8  barrels  of  flour  cost  $33f,  what  will  20 
barrels  cost  ? 

7.  If  it  require  9f  yards  of  cloth  to  make  3  coats, 
how  many  yards  will  it  require  to  make  8  coats  .'  „ 

8.  If  8  men  can  perform  a  certain  piece  of  work  in 
9f  days,  how  long  will  it  take  5  men  to  perform  the 

same?  #  • 

9.  What  will  be  the  cost  of  6  sheep,  if  15  cost  $10|? 

10.  If  1  person  consume  lOgV  bushels  of  wheat  in 
a  month,  how  much  will  13  persons  consume  in  the 

same  time  ?  /  3  C  . 

11.  If  9£  cents  will  buy  4  peaches,  what  will  be  the 

cost  of  9  peaches  ?  J  % 

12.  If  $9TV  will  pay  for  5  weeks’  board,  how  many 
dollars  will  pay  for  8  weeks’  Doard  ?  g 

13.  If  6  orifices  will  fill  a  vessel  in  3f  hours,  how 
many  of  the  same  size  will  be  required  to  fill  it  in  y'y 

of  an  hour  ?  v-  i'¬ 
ll.  If  9  men  can  build  a  boat  in  5|  days,  in  how 
many  days  could  6  men  build  it  ? 

8* 

v  .  *’ c  ..  *  j  &  *  ~  z  '' s’ 1  y 


u 


90 


SIMPLE 


PROPORTION., 

<  ■  L 


15.  If  2  men  in  4  days  can  earn  $12,  how  many  • 
dollars  can  7  men  earn  in  the  same  time  ? 

16.  If  I  pay  17§-  cents  for  riding  4  miles,  how  much 
must  I  pay  for  riding  6  miles  ?  j  t  ■ 

17.  What  will  1  year’s  board  cost,  at  $5§  for  4 

weeks?  £  Y 

18.  If  9  barrels  of  fish  cost  $54£,  what  will  27  bar¬ 
rels  cost  ?  7  -  .  v  J  j  y  ?  / !  i 

19.  How  raatiy  dollars  will  1  barrel  of  tobacco  cost, 

if  17  barrels  cost  514  eagles?  7 

20.  If  13  pounds  of  tea  cost  10|  dimes,  what  will 
5  pounds  cost? 

21.  If  7 1  tons  of  hay  keep  6  horses  through  the  I 
winter,  how  many  tons  will  keep  9  horses  the  same 
time  ? 

22.  A  fox  is  40  rods  before  a  hound  and  runs  3  rods 
to  the  hound’s  5  ;  how  many  rods  must  the  hound  run 
to  overtake  the  fox  ? 


23.  How  many  dollars  will  a  man  earn  in  14  days, 
if  he  earn  $3^  in  4  days  ? 

24.  A  merchant  bought  8  pieces  of  cloth,  each 
piece  containing  5  yards  for  $32£ ;  how  much  did  it 
cost  a  piece,  and  how  much  a  yard  ?  /  TZ  t »  1 7; 

25.  If  in  a  certain  time  6  horses  eat  14f  bushels  of 
oats,  how  many  bushels  will  8  horses  eat  in  the  same 
time  ? 

26.  A  boy  sold  3  lemons,  at  the^rate  of  6  for  8 
cents  ;  how  much  did  he  receive  for  them  ? 

27.  A  boy  gave  4^  cents  for  oranges,  at  the  rate  of 
5  oranges  for  7  4  cents ;  how  many  did  he  buy  ? 

28.  If  a  piece  of  mahogany  weighing  9  pounds,  is 
worth  $2f,  what  \s  the ;  value  of  42  pounds,  at  the 
same  rate? 

29.  If  a  pole  8  feet  long  cast  a  shadow  4f  feet,  what 
will  be  the  length  of  the  shadow  of  a  pole  which  is  15 
feet  long,  at  the  same  time  of  day  ? 

30.  At  a  certain  time  of  day,  a  pole  5  feet  long 


/ 

V 


,LI 


4 


*  /  4 

I 

REDUCTION  OF  FRACTIONS.  91 

f-  *i  4*  ~  4 - 

casts  a  shadow  7^  feet;  what  is  the  length  of  that  pole 
which  at  the  same  time,  casts  a  shadow  4£  feet  ? 

31.  If  it  require  $2 If  worth  of  provision  to  serve  8 
men  2  days,  how  many  dollar’s  worth  will  serve  5  men 
4  days  ? 

32.  Vvdiat  is  the  length  of  a  pole  the  shadow  of 
which  is  12  feet  long,  at  the  same  time,  a  pole  2f  feet 
in  length  casts  a  shadow  4  feet  long.  v 

n-<,*  2% 

1 i  ; '  i  l ; 

LESSON  XIII. 

Bemark. — By  inspecting  Lessons  8th  and  10th,  we  observe, 
that,  multiplying  both  numerator  and  denominator  by  the  same 
number,  does  not  alter  the  value  of  the  fraction.  Hence,  to 
convert  a  fraction  to  an  equivalent  fraction  having  a  different 
denominator,  we  may  multiply  both  numerator  and  denominator 
by  any  number  which  will  cause  the  fraction  to  have  the  re¬ 
quired  denominator. 

1.  James  gave  his  sister  J  of  an  apple  ;  how  many 
fourths  was  that  ? 

2.  ~  is  how  many  sixths? 

3.  Byron  gave  his  sister  \  of  an  apple,  and  his 
brother  J  of  an  apple  ;  how  many  fourths  did  he  give 
away  ? 

4.  \  is  how  many  sixths  ? 

5.  is  how  many  sixths  ? 

6.  j  and  i  are  how  many  sixths  ? 

7.  f  are  how  many  sixths? 

8.  |  are  how  many  twelfths  ? 

9.  f  are  how  many  twelfths? 

10.  J  are  how  many  eighteenths  ? 

11.  f  are  how  many  tenths  ? 

12.  §  are  how  many  tenths? 

13.  f  are  how  many  twentieths  ? 

14.  is  how  many  tenths? 

15.  Harris  gave  f  of  an  orange  to  his  sister;  how 
many  fifteenths  did  he  give  her  ? 


92  ADDITION  AND  SUBTRACTION 

16.  How  many  sixteenths  in  f  ? 

17.  How  many  sixteenths  in  f  ? 

18.  How  many  sixteenths  in  £  ? 

19.  How  many  fourteenths  in  ? 

20.  How  many  fourteenths  in  4  2 

21.  How  many  fourteenths  in  -f  ? 

22.  How  many  ninths  in  |  ? 

23.  How  many  twentieths  in  |  ? 

24.  How  many  fortieths  in  |  ? 

25.  How  many  forty-ninths  in  4  ? 

26.  How  many  fifteenths  in  |  ? 

27.  A  man  gave  }  of  a  bushel  of  potatoes  to  one 
poor  woman,  and  T3¥  of  a  bushel  to  another ;  what 
part  of  a  bushel  did  he  give  to  both  ? 

28.  How  could  you  divide  an  apple  so  as  to  give  f 
of  it  to  1  boy,  and  ~  of  it  to  another  ? 

29.  f  +  |  are  how  many  fifteenths? 

Solution. — §  equals  f6j,  and  §  equals  T65  and  4°  are 

or  HV 

30.  |  +  |  are  how  many  twelfths? 

31.  |-  +  -|  are  how  many  eighteenths? 

32.  !■  + 1  are  how  many  twenty -fourths  ? 

33.  4  arc  how  many  times  ? 

34.  What  is  the  sum  of  f  and  f  ? 

35.  What  is  the  sum  of  4  and  §  ? 

36.  What  is  the  sum  of  ~  and  f  ? 

37.  What  is  the  sum  of  f  and  f  ? 

38.  What  is  the  sum  of  4  and  f  ? 

39.  What  is  the  sum  of  4  and  §■  ? 

40.  What  is  the  sum  of  f  and  f  ? 

41.  What  is  the  sum  of  i  and  4  ? 

42.  What  is  the  sum  of  4  and  \  ? 

43.  What  is  the  sum  of  J-,  4  and  §  ? 

44.  What  is  the  sum  of  f,  |  and  f  ? 

45.  From  f  subtract  4  ? 

46.  From  f  subtract  §. 

47.  From  4  subtract  |. 


OF  FRACTIONS. 


48.  From  24  subtract  -f. 

49.  From  4  subtract 

50.  From  3  subtract  f . 

51.  From  9  subtract  -f . 

52.  From  5  subtract  |. 

53.  From  3  subtract  1^. 

54.  From  9  subtract  2|. 

55.  From  6  subtract  3f. 

*  56.  14  —  3^  are  bow  many? 

57.  7  —  2f  are  how  many? 

58.  9  —  3-|  are  how  many? 

59.  10  —  3f  are  how  many? 

60.  12  —  3|-  are  how  many? 

61.  13  —  7y*r  are  how  many? 

62.  9|  —  4i  are  how  many? 

63.  7|  — 5|  are  how  many  ? 

64.  3^—1  t  are  how  many? 

65.  4-|  — 1|  are  how  many? 

66.  5|  — 2|  are  how  many? 

—437.  9f  — 7f  are  how  many  ? 

68.  2f  +  3i  —  f  are  how  many? 

69.  4|  +  5|  —  2f  are  how  many? 

70.  3J-  +  4T  —  f  are  how  many  ? 

71.  9|  +  3f  — 3  are  how  many? 

72.  f -ff  —  a  are  how  many? 

73.  f  + 1  +  4  —  4  are  how  many  ? 

74.  2|  are  how  many  times  T2¥  ? 

75.  3|  are  how  many  times  T4o  ? 

76.  ,93  are  how  many  times  • 

77.  i  are  how  many  times  ? 

78.  -f  are  how  many  times  T\  ? 

79.  I}  are  how  many  times  y3g  ? 

80.  4  are  how  many  times  T2y  ? 

81.  T5^  are  how  many  times  ^  ? 

82.  8|  are  how  many  times  24  ? 

83.  10|  are  how  many  times  T9y  ? 

84.  I24  are  how  many  times  1|  \ 


94 


REDUCTION  or  fractions. 


85.  £  +  }  +  £  is  h°w  much  less  than  a  whole  one  ? 

86.  £+f  +  f  is  how  much  less  than  a  whole  one? 

87.  A  lady  gave  £  of  all  her  money  for  a  dress,  and 
j  of  it  for  a  shawl ;  what  part  of  her  money  had  she 
remaining. 

88.  £  of  an  army  was  killed,  and  £  taken  prison¬ 
ers  ;  what  part  of  the  army  escaped  ? 

89.  |  of  an  army  was  killed,  £  taken  prisoners,  and 
500  escaped;  how  many  were  there  in  the  army? 

90.  |  of  the  length  of  a  pole  is  in  the  ground,  £  of 
it  in  the  water,  and  12  feet  in  the  air;  what  is  the 
length  of  the  pole  ? 

-  91.  A  market  woman  sold  £  of  all  her  oranges  to 

one  man  and  £  of  them  to  another,  and  then  had  only 
9  remaining;  how  many  had  she  at  first,  and  how 
many  did  she  sell  to  each  ?  J  / 

92.  A  man,  after  spending  £  of  his  fortune,  found 

that  $20  was  £  of  what  he  had  remaining  ;  what  was 
his  fortune  ?  .  r 

93.  A  hawk  caught  |_  of  Euphemia’s  chickens,  a 
cat  killed  £  of  them,  £  of  them  died,  and  she  had  13 
remaining;  how  many  had  she  at  first,  and  how  many 
were  destroyed  by  the  hawk  and  cat  respectively  ? 

94.  Said  A  to  B  if  to  my  age  you  add  its  £  and  its  |, 
the  sum  will  be  38  ;  how  old  was  he? 

95.  A  is  40  years  old,  and  £  of  his  age  is  f  of  twice 
as  much  as  his  wife’s  age  ;  how  old  was  his  wife? 

(/  X  j  )  ~  ^ 

.  - -o- -e— - - 

M  “  3  \ 

b  a  LESSON  XIV.  ;} 


Remark. — By  inspecting  Lessons  8th  and  10th,  we  observe, 
that  dividing  both  numerator  and  denominator  of  a  fraction  by 
the  same  number,  does  not  alter  its  value.  Hence  to  reduce  a 
fraction  to  its  lowest  terms,  we  may  divide  both  numerator  and 
denominator  by  any  number  that  is  contained  in  each  of  them 
without  a  remainder. 


1. 


Reduce  £  to  its  lowest  terms, 

/  ' 


- 1 'J 


REDUCTION  OP  FRACTIONS. 


9a 


2.  Reduce  f  to  its  lowest  terms. 

3.  Reduce  f  to  its  lowest  terms. 

4.  Reduce  ff  to  its  lowest  terms. 

5.  Reduce  ff  to  its  lowest  terms. 

6.  Reduce  ff  to  its  lowest  terms. 

7.  Reduce  ff  to  its  lowest  terms. 

8.  Reduce  f  f  to  its  lowest  terms. 

9.  Reduce  ff  to  its  lowest  terms. 

10.  Reduce  ff  to  its  lowest  terms. 

11.  Reduce  f  f  to  its  lowest  terms. 

12.  Reduce  T7ff  to  its  lowest  terms. 

13.  Reduce  ff  to  its  lowest -terms. 

14.  Reduce  ff  to  its  lowest  terms. 

15.  Reduce  ff  to  its  lowest  terms. 

16.  Why  does  the  value  of  the  fraction  remain  the 
same,  when  you  divide  both  numerator  and  denominator 
by  the  same  number  ? 

(  17.  When  you  multiply  both  numerator  and  de¬ 
nominator  by  the  same  number,  why  does  it  not 
change  the  value  of  the  fraction  ? 

18.  Reduce  4  times  ff  to  its  lowest  terms. 

19.  Reduce  1  times  T\  to  its  lowest  terms. 

20.  Reduce  8  times  2f  to  its  lowest  terms. 

21.  Reduce  6  times  ff  to  its  lowest  terms. 

22.  Reduce  4  times  ff  to  its  lowest  terms. 

23.  Reduce  12  times  ff  to  its  lowest  terms. 

24.  Reduce  12  times  to  its  lowest  terms. 

25.  Reduce  8  times  to  its  lowest  terms. 

26.  Reduce  7  times  ff  to  its  lowest  terms. 

27.  Reduce  5  times  ff  to  its  lowest  terms. 

28.  Reduce  4  times  ff  to  its  lowest  terms. 

29.  Reduce  6  times  ff  to  its  lowest  terms. 

30.  Reduce  9  times  ff  to  its  lowest  terms. 


96 


COMPOUND  FRACTIONS. 


LESSON  XV. 

1.  If  you  cut  an  apple  into  two  equal  pieces,  wliat 
will  1  of  these  pieces  be  called  ? 

2.  If  you  cut  \  of  an  apple  into  two  equal  pieces, 
what  part  of  a  whole  apple  will  1  of  these  pieces  be 
called  ? 

3.  If  Alice  has  i  of  a  lemon,  and  gives  4  of  it  to 
Ann,  what  part  of  a  lemon  will  Ann  receive  ? 

Solution. — }  equals  f.  Therefore,  Ann  receives  |  of  §  of  a 
lemon,  which  is  ^  of  a  lemon. 

4.  George,  having  Y  °f  a  melon,  gave  |  of  it  to 
Marcus  ;  what  part  of  a  melon  did  Marcus  receive  ? 

5.  Crary  had  4  of  a  dollar,  and  gave  half  of  it  to 
Joshua;  what  part  of  a  dollar  did  Joshua  receive? 

6.  Robert  had  j  of  a  dollar,  and  gave  4  of  it  for  a 
cake  ;  how  many  cents  did  the  cake  cost  him  ? 

7.  Margaret  had  |  of  a  pound  of  candies,  and  Mary 
had  \  as  much  ;  how  much  had  Mary  ? 

8.  Jane  had  4  of  a  pouud  of  sugar,  and  Ann  4  as 
much;  how  much  had  Ann? 

9.  A  boy  bought  a  of  a  quart  of  chestnuts,  and 
gave  4  of  them  to  his  sister;  what  part  of  a  quart  did 
she  receive  ? 

10.  A  man  owned  |  of  a  share  in  a  bank,  and  sold 
4  of  that;  what  part  of  a  share  had  he  remaining? 

11.  B  owned  j  of  a  ship,  and  sold  4  of  his  share; 
what  part  of  a  whole  ship  did  he  sell  ? 

12.  What  is  4  0f  i‘t 

Solution. — i  of  ^  is  jR. 

13.  What  is  i  of  i? 

14.  What  is  4  of 

15.  What  is  i  of 

16.  What  is  4  of  4  ? 

17.  What  is  4  of  t? 

18.  What  is  4  of  i? 


COMPOUND  FRACTIONS. 


97 


19.  What  is  i  of  1? 

20.  What  is  TV  of  |? 

21.  A  kite  was  up  in  the  air  and  fell  f  of  the  way 
to  the  ground,  it  then  arose  £  of  its  distance  from  the 
ground  ;  what  part  of  the  whole  distance  was  it  above 
the  ground  ? 

22.  Homer  is  |  as  old  as  his  father,  and  Nelson  is 
£  as  old  as  Homer ;  what  part  of  the  father’s  age  is 
Nelson’s  age  ? 

23.  A  man,  owning  |  of  a  barrel  of  fish,  accom¬ 
modated  his  neighbor  w’ith  y  of  it ;  how  much  had  he 
remaining;  ? 

24.  A  man,  having  J-  of  an  eagle,  gave  |  of  it  to  B, 
and  B  gave  Ty  of  what  he  had  to  C  ;  vdiat  part  of  an 
eagle  had  each  after  this  division,  and  how  many  cents 
had  each  ? 

25.  Elizabeth  had  f  of  a  pie,  and  gave  ^  of  it  to 
Harriet ;  how  much  did  she  receive  ? 


i 
9 > 


Solution. — of  i  is  g ;  and  if  £  of  }  is  j,  \  of  §  is  twice 
which  are  f.  Therefore  Harriet  had  f  of  a  pie. 

Or,  Solution. — ^  of  f  is  f. 


26. 

What 

is 

1 

2 

of 

3  9 

5  • 

27. 

What 

is 

1 

4 

of 

2.  9 

3  * 

28. 

What 

is 

1 

5 

of 

2  2 

3  * 

29. 

What 

is 

1 

5 

of 

3  2 

4  • 

30. 

What 

is 

1 

7 

of 

3  2 

4  * 

31. 

What 

is 

1 

8 

of 

A  2 

5  • 

32. 

What 

is 

1 

9 

of 

2  9 

3  * 

33. 

What 

is 

1 

9 

of 

4  2 

5  • 

34. 

What 

is 

1 

8 

of 

.3  2 

6  * 

35. 

What 

is 

1 

5 

of 

3  2 

5  • 

36. 

What 

is 

4 

of 

J5_  2 

1  3  * 

37. 

What 

is 

1 

9 

of 

3  2 

8  * 

38. 

What 

is 

1 

f 

of 

1  2 

7  * 

39. 

What 

is 

i 

f 

of 

12  2 

7  ’ 

40. 

What 

is 

2 

3 

of 

1  2 

4  * 

9 


98 


3  l 

COMPOUND  FRACTIONS. 


41. 

What 

is  £ 

of 

12 

5  • 

42. 

What 

is  | 

of 

JL  2 

7  ‘ 

43. 

What 

is  f 

of 

JL  2 

9  * 

44. 

What 

is  £ 

of 

1  2 

7  * 

45. 

What 

is  £ 

of 

1  2 
s  ’ 

46. 

What 

is  £ 

of 

1  2 

9  * 

47. 

What 

is  ¥ 

of 

1  2 

4  * 

48. 

What 

is  £ 

of 

1  2 

8  * 

49. 

What 

is  4 

of 

1  2 

6  * 

50. 

What 

is  * 

of 

1  2 

4  * 

51. 

What 

is  | 

of 

3  2 

¥  * 

52. 

What 

is  } 

of 

2  2 

5  • 

53. 

What 

is  -1 

of 

2  2 

7  * 

54. 

What 

• 

!S  | 

of 

2  2 

8  " 

55. 

What 

is  | 

of 

3  2 

5  * 

56. 

What 

is  £ 

of 

i.  2 

7  ' 

57. 

What 

is  j 

of 

3.  2 

7  ‘ 

58. 

What 

is  £ 

of 

1  2 

9  * 

59. 

What 

is  4 

of 

J.  2 

7  * 

60. 

What 

1S  Ti 

of 

2  2 

3  * 

61. 

What 

part 

of 

1  i  2. 

x  x  3 

of 

1  2 

5  * 

62. 

What 

part 

of 

1  is  £ 

of 

J.  2 

6  • 

63. 

WThat 

part 

of 

2  is  £ 

of 

12 

3  * 

Solution. — 4  of  \ 

is§.  1 

is  JL  of  2.  If  1 

is  £ 

of  2,  £ 

i,  or  T*B 

of  2,  and 

|  are  2  times 

Vgj  or  ^  °f 

2. 

64. 

What 

part 

of 

2  is  j 

of 

1£? 

65. 

What 

part 

of 

2  is  | 

of 

1  2 

3  * 

66. 

AVhat 

part 

of 

3  is  £ 

of 

1  2 

2  * 

67. 

What 

part 

of 

4  is  £ 

of 

U  2 

±  5  * 

68. 

What 

part 

of 

5  is  1 

of 

2  2 

3  * 

69. 

AVhat 

part 

of 

9  is  £ 

of 

11  2 

A  3  ’ 

70. 

What 

part 

of 

2  is  £ 

of 

Ji  2 

4  * 

71. 

AVhat 

part 

of 

2  is  £ 

of 

2i  ? 

72. 

AVhat 

part 

of 

4  is  £ 

of 

3_  2 

0  • 

73. 

AVhat 

part 

of 

6  ’  is  £ 

of 

1  2 

6  * 

74. 

AVhat 

part 

of 

3  is  £ 

of 

42  2 
* 5  * 

99 


compound  fractions. 


t  of  I2ff 
2  of  10#  ? 


75.  What  part  of  '4  is 

76.  What  part  of  7  is  ?  ux  1UA, 

}77'  Anthony  had  i  of  |  of  a  pound  of  cinnamon: 
what  part  of  a  pound  had  he  ?  ! 

78.  Albert  lmd  j  of  f  of  a  quart  of  strawberries ; 
how  many  strawberries  had  he,  provided  1  quart  con- 
tamed  42  strawberries  ?  ^ 

A^nc!  Savc  t  of  -f  of  a  melon  to  his  brother; 
wnat  part  of  a  melon  had  he  remaining? 

80.  Matilda  bought  #  of  a  quart  of  milk  for  tea, 

and  spilled  3  of  it ;  what  part  of  a  quart  had  she  re- 
maimng  ? 

81.  Edwin  picked  J  of  a  pail-full  of  blackberries, 
and  on  bis  way  home  spilled  i  of  them  ;  what  part  of 
a  paii-full  had  he  remaining  ? 

82.  A  merchant  bought  f  of  a  hogshead  of  molasses, 

and  j  of  it  leaked  out ;  what  part  of  a  hogshead  had 
ne  remaining?  ° 

t  83-  Mirriam  had  |  of  a  pound  of  candies,  and  gave 

t  of  them  to  Augusta ;  what  part  of  a  pound  did  she 
give  Augusta?  L 

84.  Elisha  found  If  and  gave  |  of  it  to  Ephraim; 
^hat  pait  of  a  dollar  had  he  remaining? 

So.  Andrew  bought  |  of  a  pound  ^of  maple-sugar, 
and  gave  t  of  it  to  Walter ;  what  part  of  a  pound  did 

86.  Jacob,  having  a  pine-apple,  gave  f  of  4  of  it 
to  the  one  that  could  tell  how  much  that  would  be  • 
wnat  part  of  a  melon  had  Jacob  remaining? 

87.  James  gave  f  of  f  of  a  dime  for  a’top ;  how 
much  did  the  top  cost  him  ? 

88.  Robert  gave  f  of  a  dollar  for  a  cap  ;  how  much 
did  the  cap  cost  him  ? 

89.  Mary  gave  }  of  If  dimes  for  a  comb;  how 
many  cents  did  the  comb  cost  her? 

90.  Clarinda  gave  f  of  6  dimes  for  a  pair  of  gloves : 
how  many  cents  did  the  gloves  cost  her  ? 


100 


SIMPLE  PROPORTION. 


91.  A  man,  having  4f  barrels  of  flour,  sold  -  of  it  5 

how  much  remained  unsold  ?  ■ ■ 

92.  A  man  gave  f  of  $31  for  a  silver  pencil ;  what 

was  the  cost  ot  the  pencil  ?  . 

93  Jane  worked  8f  hours  m  a  day,  and  Delilah 
worked  only  f  as  many;  how  many  hours  did  she 

work  in  a  day  ?  . 

94.  B  gave  $32§  for  a  cow,  which  was  f  as  much 

as  A  gave  for  his ;  how  much  more  did  B’s  cow  cost 


than  A’s  ?  _  .  .  .  , , 

95.  Darius  is  18£  years  old,  and  Daniel  is  f  as  old; 

how  old  is  he  ?  ...  „ 

96.  If  1  yard  of  cloth  cost  $5f,  what  will  f  ot  a 


veil'd  cost  ? 

97.  If  4  yards  of  cloth  cost  $9£,  what  will  f  of  a 


yard  cost  ? 

98.  If  5  barrels  of  beef  cost  $18£,  what  will  i  of  a 


"barrel  cost  ? 

99.  If  |  of  an  apple  cost  f  of  a  cent,  what  will  1 
apple  cost  ? 

100.  If  d  of  an  orange  cost  14  cents,  what  will  Te 
of  an  orange  cost? 

101.  If  4  pounds  of  butter  cost  6J-  dimes,  how  many 
cents  will  If  pounds  cost? 


- 

LESSON  XVI. 

1.  If  4  barrels  of  flour  cost  $14§,  wThat  will  f  of  a 

cost »  • 

2.  If  3  bushels  of  potatoes  cost  5|  dimes,  what  will 

14  bushels  cost  ? 

3.  If  21  bushels  of  apples  cost  dimes,  how  many 

cents  will  4  of  a  bushel  cost  ?  ... 

4.  If  f  of  an  apple  cost  |  of  a  cent,  wrkat  will  1 

apple  cost  ? 


DIVISION  OP  FEACTIONS. 


101 


5.  If  f  of  an  orange  cost  £  of  a  cent,  what  will  -3 

of  an  orange  cost  ?  4 

6.  If  2£  yards  of  cassimere  cost  $3£,  what  will  5\ 

yards  cost?  2 

V.  If  5f  yards  of  shalloon  cost  $5T\,  what  will  2 
yards  cost  ? 

8.  II  in  3-f  hours,  A  can  do  a  certain  piece  of  work, 
how  long  will  it  take  him  to  do  a  piece  of  work  12. 
times  as  large  ?  5 

9  £  of  A's  age  is  f  of  B’s;  and  £  of  B’s  age  is  f 
oi  C  s  age.  How  old  are  A  and  B  respectively,  pro¬ 
vided  C  is  81  years  old  ? 

10  Bought  3|  boxes  of  goods,  at  $6/r  a  box,  and 

paid  for  it  with  sheep,  at  $2  a  head ;  how  many  sheep 
did  it  take  ?  J  1 

11.  How  many  times  f  is  £  ? 


Solution.— 1  is  contained  in  £,  f  times ;  and,  if  l  is  con. 
tamed  in  £,  f  times,  1  is  contained  in  £  5  times  £  times,  whict 
are  \5-  times,  and  f  is  contained  in  it,  \  of  \5-  times,  which  is 
V-  times,  or  1  \  times. 


12. 

How 

many 

times 

2 

3 

is 

3  2 

4  * 

13. 

How 

many 

times 

2 

"3 

is 

1  2 

8  • 

14. 

How 

many 

times 

3 

5 

is 

-6  2 

7  * 

15. 

How 

many 

times 

3 

8 

is 

-JL  2 
16* 

10. 

How 

many 

times 

2 

X 

is 

l±  2 

3  * 

17. 

How 

many 

times 

2 

7 

is 

-JL  2 

14* 

18. 

How 

many 

times 

2 

X 

is 

1  2 

8  * 

19. 

How 

many 

times 

4 

5 

is 

93  ? 

°  7  • 

20. 

How 

many 

times 

3 

4 

is 

2f? 

21. 

How 

many 

times 

3 

7 

is 

2f? 

22. 

How 

many 

times 

5 

9 

is 

55  2 

23. 

IIow 

many 

times 

o 

X 

is 

JL  2 

10* 

24. 

How 

many 

times 

4 

7 

is 

JL2  2 

1  4  • 

3i? 

25. 

IIow 

many 

times 

5 

0 

is 

26. 

How 

many 

times 

7 

8 

is 

41  2 

27. 

How 

many 

times 

9* 

H 

is 

2±  2 

^2  • 

102 


DIVISION  i 

OF  FRACTIONS. 

28. 

How 

many 

times 

2f 

is 

11  % 

A5  * 

29. 

How 

many 

times 

H 

is 

51  2 

°5  * 

30. 

How 

many 

times 

42 

3 

is 

53  2 

31.  A  farmer  sold  a  quantity  of  rye  for  $96,  which 
was  only  f  of  what  it  was  worth  ;  how  much  did  he 
lose  by  the  bargain  ? 

32.  A  man  sold  a  cow  for  If  times  what  she  cost 
him,  and  by  so  doing  gained  $6  ;  how  much  did  the 
cow  cost  him  ? 

33.  A  merchant  sold  a  quantity  of  goods  for  ||  of 
what  they  cost,  and  by  so  doing,  he  lost  $15  ;  how 
much  did  the  goods  cost  him  ? 

34.  A  farmer,  having  lost  12  sheep,  found,  that  only 
•J  of  his  flock  remained  ;  how  many  sheep  had  he  re¬ 
maining  ? 

35.  An  individual  being  asked  how  many  geese  he 
had,  answered,  that  if  to  of  his  flock  24  geese  were 
added,  the  sum  would  equal  If  times  his  original 
flock ;  how  many  geese  had  he  ? 

36.  If  |  of  a  yard  of  cloth  cost  $f,  what  will  f  of  a 
yard  cost  ? 

37.  A  boy,  being  asked  his  age,  said,  that  8f  years 
was  |  of  twice  as  much  as  his  age  ;  how  old  was 
he? 

38.  If  |  of  the  candies  I  have  cost  7f  cents,  what 
will  f  of  them  cost  ? 

39.  What  will  f  of  a  barrel  of  flour  cost,  if  f  of  a 
barrel  cost  $2f  ? 

40.  What  will  -f  of  an  orange  cost,  if  f  of  an  orange 
cost  2 f  cents  ? 

41.  How  many  yards  of  cloth  will  be  required  to 
make  a  coat,  if  1|  yards  will  make  f  of  a  coat? 

42.  |-  of  2  are  now  many  times  f  ? 

43.  of  8  arc  how’  many  times  \  ? 

44.  |  of  7  arc  how  many  times  3  ? 

45.  f  of  8  are  how  many  times  f  ? 

46.  |  of  12  are  how  many  times  §  of  6  ? 


FRACTIONS. 


103 


47.  f  of  7  are  how  many  times  f  of  2  ? 

48  If  §  of  3  yards  of  cloth  cost  $1J,  what  will  f  of 
7  yards  cost  ?  5 

jit9,  *£  I  of  ®  yards0of  clo«i  cost  $2f,  how  much 
Will  |  of  7  yards  cost  ? 

1  nf°2  1 f  °/  a  bf1TeI  °f  flour  cost  what  will 

2  °1  f  of  |  of  a  barrel  cost  ? 


LESSON  XVII. 


1.  12 


f  of 


what  number  ? 

Solution.  Iff  of  some  number  is  12,  I  of  that  number  is  l 

0  1  ft  0r  mi!  atK  *T  whicJl  is  that  number,  are  4  times  4  which 

ATfi  l  r  Therefore  12  is  £  of  16. 


are  16 

2, 

3, 

4, 

6. 

'7. 

8. 

9. 

10. 

11. 

12. 

13. 

14. 

15. 
1G. 

17. 

18. 

19. 

20. 


15 

18 

20 

26 

25 

30 

32' 

36 

36 

36 

24 

9 

12 

38 

16 

16 

16 

40 

40 


is 

is 

is 

is 

is 

is 

is 

is 

is 

is 

is 

is 

is 

is 

is 

is 

is 

is 

is 


3 
5 
2 
T 

4 

5 
2 
3 
J> 

7 

£. 

8 
8 
9 
6. 

7 

_6 

1  1 

£ 

2 

£ 

7 

£ 

7 

A 

5 

£ 

3 

A 

5 

4. 

7 
2 
5 

5. 

8 

£ 

9 


of  what  number? 
of  what  number? 
what  number? 


of 

of 

of 

of 

of 

of 

of 

of 

of 

of 

of 

of 

of 

of 

of 

of 

of 


Solution.— 40  is  £  of  45. 


what 

what 

what 

what 

what 

what 

what 

Avhat 

what 

what 

what 

what 

what 

what 

what 

what 


number? 
number? 
number  ? 
number  ? 
number  ? 
number  ? 
number  ? 
number  ? 
number  ? 
number  ? 
number? 
number  ? 
number  ? 
number  ? 
number  ? 
number  ? 


nJ^n»K;iUWihen  PT.ls  are  famiUar  With  the  analysis  of  these 
solution  ’  ^  termed|ate  steps  ma^  be  omit‘cd,  as  in  the  above 


104 


FRACTIONS. 


21.  72  is  f  of  what  number? 

22.  72  is  t9o  of  what  number  ? 

23.  12  is  |  of  how  many  times  2? 

24.  16  is  |  of  how  many  times  3  ? 

25.  18  is  f  of  how  many  times  9  ? 

26.  32  is  4  of  how  many  times  4  ? 

27.  46  is  §  of  how  many  times  23  ? 

28.  48  is  |  of  how  many  times  5  ? 

29.  48  is  4  of  how  many  times <4  ? 

30.  36  is  4  of  how  many  times  2  ? 

31.  30  is  |  of  how  many  times  4  of  12  ? 

32.  30  is  4  of  how  many  times  4  of  10? 

33.  16  is  f  of  how  many  times  |  of  9  ? 

34.  16  is  T\  of  how  many  times  f  of  16  ? 

35.  24  is  f  of  how  many  times  |  of  12? 

36.  25  is  f  of  how  many  times  4  of  9  ? 

37.  35  is  t53  of  how  many  times  f  of  9  ? 

38.  40  is  f  of  how  many  times  f  of  10  ? 

39.  48  is  T%  of  how  many  times  |  of  25? 

40.  96  is  |  of  how  many  times  f  of  16  ? 


LESSON  XVIII. 

1.  |  of  6  is  f  of  what  number  ? 

2.  a  of  10  is  f  of  what  number? 

3.  |  of  8  is  f  of  what  number  ? 

4.  4  of  21  is  f  of  what  number? 

5.  4  of  15  is  T\  of  what  number? 

6.  y3_  of  40  is  f  of  what  number  ? 

7.  A  of  27  is  |  of  what  number? 

8.  |  of  27  is  t83  of  what  number? 

9.  |  of  81  is  t9o  of  what  number? 

10.  4  of  49  is  t6t  of  what  number? 

11.  |  of  12  is  4  of  how  many  times  2  ? 

12.  |  of  16  is  |  of  how  many  times  2  ? 

13.  |  of  10  is  4  of  how  many  times  4  ? 


fractions. 


105 


14.  I  of  16  is  ^5  of  liow  many  times  6  ? 

15.  jr  ot  15  is  f  of  how  many  times  6  ? 

16.  |  of  20  is  |  of  how  many  times  3  ? 

17.  £  of  12  is  §  of  how  many  times  5  ? 

18.  |  of  20  is  f  of  how  many  times  3  ? 

19.  £  of  36  is  f-i  of  how  many  times  4  ? 

20.  |  ot  72  is  |  of  how  many  times  12  ? 

Solution.— |  of  72  is  64.  64  is  f  of  96.  96  is  8  times  12. 

21.  f  of  96  is.  |  of  how  many  times  90  ? 

22.  f-  of  117  is  f  of  how  many  times  4  ? 

23.  £  of  56  is  £  ot  how  many  times  8  ? 

24.  £  of  60  is  |  of  how  many  times  5  ? 

25.  £  ot  36  is  |  of  how  many  times  12  ? 

26.  £  of  72  is  £  of  how  many  times  5  ? 

27.  f  of  40  is  T5^  of  how  many  times  21  ? 

28.  f  of  32  is  4.  of  how  many  times  9  ? 

29.  £  of  15  is  £  of  how  many  times  2  ? 

30.  £  of  15  is  £  of  how  many  times  9  \ 

31.  f  of  24  is  £  of  how  many  times  3  ? 

32.  £  of  45  is  £  of  how  many  times  3  ? 

33.  5  of  14  is  |  of  how  many  times  5  ? 

34.  i  of  18  is  f  of  how  many  times  7  ? 

35.  T9-  of  40  is  £  of  how  many  times  6  ? 

36.  |  of  45  is  T6T  of  how  many  times  3  ? 

37 .  £  of  35  is  £  of  how  many  times  2  ? 

38.  |  of  81  is  i  of  how  many  times  9  ? 

39.  |  of  5  is  £  of  how  many  times  7? 

40.  f  of  7  is  f  of  how  many  times  3  ? 

41.  11  s  horse  cost  $>60,  and  ~  of  the  cost  of  the 
lorsc,  is  y  of  two  times  the  value  of  his  wagon  ;  what 
is  the  value  of  his  wagon  ? 

•  ^  coat  cost  $20,  and  £  of  the  cost  of  the  coat 

is  f  of  .8  times  the  price  of  a  hat ;  the  price  of  the  hat 

is  required  ? 

.  43-  a  cow  cost  $30,  and  |  of  this,  is  f  of  10 
times  the  price  of  a  sheep ;  what  is  the  price  of  a 
sheep  ? 


106 


FRACTIONS. 


44.  A’s  farm  is  worth  $1200,  and  §  of  its  value,  is 
|  of  10  times  the  value  of  its  yearly  productions; 
what  is  the  value  of  the  yearly  productions  ? 

45.  The  articles  contained  in  a  certain  store  cost 
$500,  and  T3F  of  their  cost  is  |  of  3  times  the  amount 
paid  for  the  silks ;  how  much  was  the  cost  of  the 
silks,  and  of  the  other  articles  respectively  ? 

46.  A’s  wedding  clothes  cost  $180,  and  f-  of  the 
cost  of  his  clothes,  is  f  of  6  times  the  cost  of  his 
wife’s  wedding  dress  ;  how  much  was  the  cost  of  her 
dress  ? 

47.  The  insurance  of  a  ship  amounted  to  $800,  and 
t  of  that  is  -^0  °f  ^  times  the  value  of  the  cargo  ; 
what  is  the  value  of  the  cargo  ? 

48.  A’s  house  cost  $1400,  and  f  of  its  cost,  is  3^ 
times  t  of  the  cost  of  the  furniture  contained  in  it ; 
what  was  the  cost  of  the  furniture  ? 

49.  Provided  a  house  was  worth  $1200,  and  f  of  its 
value  was  §  of  \  times  the  value  of  the  farm  on  which 
it  stood  ;  what  was  the  value  of  the  farm  ? 

50.  If  a  sleigh  cost  $100,  what  would  be  the  cost  of 
a  wagon,  if  §  of  the  cost  of  the  sleigh  was  T2T  of  twice 
the  cost  of  a  wagon  ? 

51.  Lambert  is  worth  $2500,  and  of  his  fortune  is 
3T  times  t  of  Latham’s  fortune  ;  how  much  is  Latham 
worth  ? 

Distances  on  the  Railroad  between  Albany  and  Buffalo. 

52.  The  distance  from  Albany  to  Schenectady,  is 
16  miles,  and  f  of  this  distance,  is  f  of  t  times  the 
distance  from  Albany  to  Rome  ;  what  is  the  distance 
to  Rome  ? 

53.  Fort-Plain  is  56  miles  from  Albany,  and  ^  of 
this  distance  is  If  times  of  the  distance  from  Al¬ 
bany  to  Rochester ;  what  is  the  distance  to  Rochester  ? 

54.  Waterloo  is  192  miles  from  Albany,  and  f-  of 
this  distance  is  If  times  the  distance  from  Albany 


FRACTIONS. 


107 


to  Utica,  and  3  miles  more ;  what  is  the  distance  to 
Utica? 

.  55*  Buffalo  is  325  miles  from  Albany,  and  f  of  this 
distance  is  7 ~  times  of  the  distance  to  Batavia,  and 
5  miles  more  ;  what  is  the  distance  from  Albany  to 
Batavia  ?  '  J 

Distances  on  the  Railroad  between  Albany  and  Boston. 

56.  Boston  is  200  miles  from  Albany,  and  |  of  this 
distance,  is  ly  times  4-  of  the  distance  to  West  Spring- 
field  ;  what  is  the  distance  to  West  Springfield  ? 

57.  From  Albany  to  the  State  line  is  38  miles,  and 

1  \  times  this  distance,  is  times  j  of  the  distance  to 
Wilbraham  5  what  is  the  distance  to  Wil  brail  am  ? 

58.  Kinderhook  is  16  miles  from  Albany,  and  £  of 
this  distance,  is  ~  times  of  the  distance  to  Dalton  5 
what  is  the  distance  to  Dalton  ? 

59.  Brighton  is  195  miles  from  Albany,  and  |  of 
this  distance  is  £  of  2  times  the  distance  to  Worcester 5 
what  is  the  distance  to  Worcester  ? 

_  60.  Grafton  is  162  miles  from  Albany,  and  f  of  this 
distance  is  —  of  3  times  the  distance  to  Westfield,  less 

2  miles  ;  how  far  is  it  to  Westfield  ? 


LESSON  XIX. 

1.  f  of  9  is  |-  of  how  many  times  £  of  25  ? 

2.  £  of  16  is  1  of  how  many  times  ~  of  21  ? 

3.  I  of  40  is  |  of  how  many  times  \  of  16  ? 

4.  |  of  80  is  |  of  how  many  times  £  of  21  ? 

5.  |  of  36  is  l  of  how  many  times  £  of  12  ? 

6.  of  45  is  £  of  how  many  times  £  of  14? 

7.  f  of  30  is  |  of  how  many  times  \  of  10? 

8.  of  48  is  i  of  how  many  times  £  of  7  ? 

9.  |  of  45  is  |  of  how  many  times  £  of  8  ? 


Solution.— |  of  45  is  36.  36  is  §  of  162. 

is  27  times  6. 


£  of  8  is  6. 


162 


108 


FRACTIONS. 


ylO.  f  of  35  is  i  of  how  many  times  |  of  11|? 

11.  £  of  54  is  f  of  how  many  times  |  of  10f  ? 

12.  |  of  25  is  |  of  how  many  times  f  of  10  ? 

13.  \  of  28  is  |  of  how  many  times  |  of  25? 

14.  £  of  18  is  |  of  how  many  times  f  .of  12  ? 

15.  £  of  36  is  £  of  how  many  times  £  of  12  ? 

16.  ft  of  54  is  I  of  how  many  times  £  of  16  ? 

lV.  i  of  32  is  §-  of  how  many  times  f  of  9  ? 

18.  |  of  108  is  |  of  how  many  times  §  of  §  of  15  ? 

19.  £  of  40  is  t52  of  how  many  times  f  of  f  of  20? 

20.  £  of  20  is  |  of  how  many  times  |  of  £  of  12  ? 


LESSON  XX. 

1.  If  1  horse  eat  £  of  a  hush  el  of  oats  in  1  day, 
how  many  horses  will  eat  a  bushel  in  the  same 
time  ? 

2.  If  the  wages  of  8  weeks  amount  to  $48,  what 
will  the  wages  of  2£  weeks  amount  to  ? 

3.  A  ship’s  crew  of  12  men  have  provision  for  5 
months  ;  how  man}?-  months  will  it  last  5  men  ? 

4.  A  man  gained  $14  by  selling  a  watch  for  If 
times  what  it  cost  him ;  how  much  did  it  cost  him  ? 

5.  There  is  a  pole,  £  of  its  length  is  under  wrater, 
and  9  feet  out ;  how  long  is  the  pole  ? 

6.  A  pole  is  standing  in  the  water,  so  that  15  feet 
is  above  the  water,  which  is  £  of  the  whole  length  of 
the  pole  ;  how  long  is  the  pole? 

7.  If  |  be  2  what  will  2  be  ? 

8.  If  8  horses  can  in  1  day  eat  4  bushels  of  oats, 
in  how  many  days  can  1  horse  eat  1  bushel  ? 

9.  If  3  horses  can  in  1  day  eat  If  bushels  of  oats, 
how  many  bushels  can  1  horse  eat  in  4  days  ? 

10.  If  1  horse  in  2  days  can  eat  6  bushels  of  corn, 
how  many  bushels  will  4  horses  eat  in  3  days  ? 


COMPOUND  PROPORTION. 


109 


11.  If  4  horses  eat  10  bushels  of  grain  in  2  days, 
how  many  bushels  will  3  horses  eat  in  12  days  ? 

12.  How  many  tons  of  hay  will  3  horses  consume 
in  4  days,  if  4  horses  in  {  of  a  day  consume  f  of  a 
ton  ? 

13.  How  many  hundred  weight  of  hay  can  3  horses 
consume  in  25  days,  if  2  horses  in  J-  of  a  day  consume 
4^-g-  of  a  hundred  weight  ? 

14.  In  how  many  days  can  4  men  cut  16  cords  of 
wood,  if  1  man  in  1  day  cut  |  of  a  cord  ? 

15.  How  many  men  will  be  required  to  earn  20 
dimes  in  4  days,  if  4  men  in.  2f  days  earn  11  dimes  ? 

10.  If  it  require  6  days  for  2  men  to  lay  36  rods  of 
wall,  how  many  men  can  in  t  of  the  time  build  72  rods 
of  similar  wall  ? 

17.  It  in  4  days  3  men  accomplish  a  certain  piece 
of  work,  how  many  men  will  be  required,  to  perform 
a  piece  of  work  4  times  as  large  in  2  days? 

18.  If  4  men  in  8  days  perform  a  certain  piece  of 
work,  how  many  men  will  be  required  to  accomplish 
3  times  as  much  work  in  f  of  a  day  ? 

19.  It  1  horse  eat  1  bushel  of  oats  in  4  days,  in 
how  many  days  would  0  horses  eat  48  bushels? 

20.  If  f  of  0  be  3,  what  will  t  of  40  be  ? 

21.  If  3  be  |  of  6,  what  will  ±  of  40  be  ? 

22.  If  2  men  in  }  of  a  day  earn  T52  of  a  dollar,  in 

how  many  days  can  3  men  earn  f  of  a  dollar  ? 

23.  If  it  require  of  a  bushel  of  oats  to  feed  4 
horses  {  of  a  day,  how  many  horses  would  it  require 
to  consume  9  bushels  in  f  of  a  day  ? 

Suggestion.- — Review  unless  the  pupils  thoroughly  under¬ 
stand  the  preceding  Chapters. 

The  study  of  Chapter  VII.  may  he  omitted  until  the  class 
has  learned  Chapter  VIII.,  (excepting  the  miscellaneous  ques¬ 
tions.) 


110 


questions. 


CHAPTER  VII. 

LESSON  I. 

1.  $24  is  |  of  twice  as  much  as  a  cask  of  wine 
cost ;  what  did  the  wine  cost  ? 

2.  Bought  30  barrels  of  flour,  and  f  of  the  num¬ 
ber  of  barrels,  equaled  4  as  many  dollars  as  they  all 
cost ;  what  did  1  barrel  cost  ? 

3.  35  is  f  of  how  many  times  §  of  4  ? 

4.  A  farmer,  being  asked  how  many  sheep  he  had, 
answered,  that  160  was  §  of  10  times  his  number; 
how  many  sheep  had  he  ? 

5.  Mr.  B,  being  asked  the  value  of  his  horse,  said, 
$54  is  t6t  of  3  times  its  value ;  what  is  the  value  of 
his  horse  ? 

6.  72  is  f  of  how  many  times  f  of  12  ? 

7.  36  is  |  of  how  many  times  §  of  12  ? 

8.  48  is  |  of  how  many  tknes  \  of  18  ? 

9.  56  is  f  of  how  many  times  %  of  8  ? 

10.  60  is  |  of  how  many  times  f-  of  16  ? 

11.  84  is  L2-  of  how  many-  times  ^  of  25  ? 

12.  A  spent  $60,  which  was  f  of  4  times  as  much 
as  he  was  worth  ;  how  much  wras  he  worth? 

13.  B  sold  9  sheep,  which  was  T\  times  ]•  of  his 
whole  flock;  how  many  sheep  had  he  remaining? 

14.  D,  at  a  game  of  cards,  lost  $20,  which  was  4 

times  f  of  all  the  money  he  had  ;  how  much  had 
he  ?  •  . 

15.  C  found  $45,  which  ivas  f  of  3  times  as  much 
as  he  already  had;  how  much  more  did  he  find  than 
he  had  at  first  ? 

16.  A  boy  lost  9  marbles,  which  was  |  of  twice  as 
many  as  he  had  at  first ;  how  many  had  he  left  ? 

17.  A  boy  gave  away  8  apples,  which  was  4  of 


QUESTIO  NS. 


Ill 


twice  as  many  as,  lie  had  left ;  how  many  had  he  at 
first  ? 

18.  12  is  |  times  of  what  number? 

19.  36  is  t6t  times  f  of  how  many  times  £  of  13^  ? 

20.  Jeremiah  is  18  years  old,  and  his  age  is  £  times 
|  of  his  father’s  age  ;  how  old  is  his  father  ? 

21.  Mary  gave  6  cents  for  a  comb,  which  was  f 
times  j  of  all  her  money  ;  how  many  cents  had  she  ? 

22.  Martha  gave  8  cents  for  a  pine-apple,  which  was 
f  times  |  of  all  her  money  ;  how  many  apples  could 
she  have  bought  with  the  money  she  had  remaining, 
at  2  cents  apiece  ? 

23.  Henry  had  20  marbles,  which  was  |  of  twice  as 
many  as  Harry  had  ;  how  many  had  Harry  ? 

24.  Margaret  is  16  years  old,  and  her  age  is  §  of  3 
times  Martha’s  age  ;  how  old  is  Martha? 

25.  |  is  |  of  twice  as  much  as  what  number  ? 

26.  A  man  bought  a  horse  for  $60,  which  was  £  of 
twice  as  much  as  he  sold  him  for;  how  much  did  he 
gain  by  the  bargain? 

27.  A  horse  was  sold  for  $40,  which  was  £  times 
of  what  he  was  worth  ;  what  was  the  value  of  the 

horse  ? 

28.  A  man  when  he  was  married,  was  20  }mars  of 
age,  which  was  £  times  £  of  the  age  of  his  wife ;  how 
old  was  she  ? 

29.  Shepherd  was  worth  $160,  which  was  £  times 
tV  of  his  father’s  fortune  ;  what  was  the  father’s 

1  u  7 

fortune  ? 

30.  A  and  B  were  playing  cards,  B  lost  $14  which 
was  t7¥  times  |  as  much  as  A  then  had  ;  and  when 
they  commenced  f  of  A’s  money  equaled  £  of  B’s. 
IIow  much  had  each  when  they  began  to  play  ? 

31.  A  and  B  were  playing  cards,  A  lost  $20  which 
was  T\  of  the  number  of  dollars  B  then  had  more 
than  A  ;  provided  this  sum  was  1£  times  as  much  as 
A  had  at  first,  how  much  had  each  when  they  began 
to  play  ? 


112 


QUEST  I  O.NS. 


LESSON  II. 


1.  A  boy,  after  spending  f  of  all  liis  money,  found, 
that  16  cents  was  all  be  bad  remaining;  bow  much 
bad  be  at  first? 


Solution. — Let  |  equal  the  money  he  had  at  first.  Then 
after  spending  £  of  it.  he  had  remaining  |  which  is  f. 
This  by  the  condition  of  the  question  is  16  cents.  If  ^  of  the  money 
he  had  at  first  is  16  cents,  ±  of  it  is  i  of  16  cents,  which  is  8 
cents;  and  3,  or  what  he  had  at  first,  are  5  times  8,  or  40  cents. 

Solution  2d. — He  spent  §  of  his  money ;  therefore,  he  had 
remaining  §  of  it,  which  equals  16  cents.  If  f  of  his  money  is 
16  cents,  he  must  have  had  40  cents. 


2.  Ruth,  after  losing  f  of  all  lier  roses,  bad  only  3 
remaining  ;  how  many  had  she  at  first  ? 

3.  Jane  gave  f  of  all  her  flowers  to  Ann,  and  bad 
4  remaining  ;  bow  many  did  she  give  to  Ann  ? 

4.  George,  after  eating  T9¥  of  all  Lis  oranges,  bad 
only  8  oranges  remaining ;  bow  many  bad  be  at 
first  ? 


5.  A  boy  expended  4  of  bis  money  for  a  pie,  f  for 
a  ball,  |  for  a  top,  and  bad  6  cents  remaining  ;  bow 
many  cents  bad  be  at  first  ? 

G.  In  a  certain  school  4  of  the  scholars  study  gram¬ 
mar,  4  study  arithmetic,  and  the  remainder,  which  is 
10,  study  geography  ;  bow  many  scholars  in  all,  and 
bow  many  attending  to  each  study  ? 

7.  A  third  part  of  an  army  wras  killed,  4  part  taken 
prisoners,  and  300  escaped ;  bow  many  was  there  in 
the  army  ? 

8.  If  from  my  age  you  subtract  \  and  §  of  my  age 
the  remainder  is  2  years  ;  bow  old  am  I  ? 

9.  B,  being  asked  bow  many  pigeons  be  caught, 
said,  that  if  to  -f  of  the  number,  36  were  added,  the 
sum  would  equal  twice  the  number.  How  many  did 
be  catch  ? 


QUESTIONS. 


113 


10.  If  to  |  of  the  cost  of  B’s  horse  yon  add  $100, 
the  sura  will  be  twice  the  cost  of  the  horse  ;  what  was 
the  cost  of  the  horse  ? 

11.  A  gentleman,  after  spending  -2  of  his  fortune  and 
i  of  the  remainder,  had  $2400  remaining  ;  what  was 
his  fortune  ? 

12.  A  gambler  lost  £  of  all  his  money,  and  the 
next  night  he  won  §-  as  much  as  he  lost  the  night 
before ;  he  then  had  $90 :  how  much  had  he  at 
first  ? 

13.  John  had  stolen  from  him  f  of  his  money,  and 
the  thief  was  not  caught  until  he  had  spent  j-  of  it; 
the  remainder,  which  was  $40  less  than  John  had 
remaining,  was  given  back ;  how  much  money  had 
John  at  first  ? 

14.  A  traveler  had  stolen  from  him  £  of  all  his 
money,  and  the  thief  was  not  caught  until  he  had 
spent  |  of  it,  the  remainder  ($100)  was  given  back; 
how  much  had  he  at  first? 

15.  If  to  i  of  the  cost  of  A’s  watch  you  add 
$10,  the  sum  will  be  $21  ;  what  was  the  cost  of  his 
watch  ? 

16.  If  to  |  of  B’s  age  you  add  15  years,  the  sum 
would  be  39  years  ;  how  old  is  B  ? 

17.  A  drover  being  asked  how  many  sheep  he  had, 
said,  if  to  i  of  my  flock  you  add  the  number  9£,  the 
sum  will  be  99^;  how  many  sheep  had  he? 

18.  ^  of  the  length  of  a  pole  is  in  the  water,  and 
12  feet  in  the  air ;  how  long  is  the  pole  ? 

19.  If  to  \  of  A’s  age  you  add  16  years,  the  sum 
will  be  1-i  times  his  age  ;  how  old  is  he? 

20.  A  man,  being  asked  how  many  pigeons  he 
caught,  replied,  if  to  f  of  the  number  I  caught  you 
add  20,  the  sum  would  lack  4  of  being  equal  to  li 
times  the  number ;  how  many  did  he  catch  ? 

10* 


114 


PARTNERSHIP. 


LESSON  III. 

1.  Divide  tlie  number  36  into  two  parts,  wliich  sliall 
be  to  each  other  as  7  to  2. 

Solution. — Since  the  two  parts  are  to  be  to  each  other  as  7 
to  2,  we  must  divide  36  into  7  +  2,  which  are  9  equal  parts ;  and 
7  of  the  parts  will  be  one  of  the  numbers,  and  2  of  them  the 
other,  a.  of  36  is  4,  and  7.  are  7  times  4,  which  are  28  (the  first 
number,)  and  §  are  2  times  4,  which  are  8  (the  other  number.) 
Or,  in  the  latter  part  of  the  solution,  say ;  ^  of  36  is  28,  the 
first  number;  and  f  of  36  is  8,  the  other  number. 

2.  Two  men  hired  a  pasture  for  $72  ;  one  put  in  7 
horses,  and  the  other  2  horses ;  what  ought  each  to  pay  ? 

3.  A  and  B  hired  a  pasture  for  $14  ;  A  put  in  4 
cows,  and  B  put  in  3  cows  ;  what  ought  each  to  pay  ? 

4.  A  and  B  bought  a  lottery  ticket  for  $5  ;  A  paid 
$3,  and  B  paid  $2.  They  drew  a  prize  of  $60  ;  what 
was  each  one’s  share  ? 

5.  Two  men  bought  40  mules :  the  first  paid  $5  as 
often  as  the  other  $3.  How  many  mules  ought  each 
to  receive  ? 

6.  Mary  and  Elizabeth  went  to  school  80  days,  and 
as  often  as  Mary  went  3  days,  Elizabeth  went  5  days ; 
how  many  days  did  each  go  ? 

7.  Reuben  had  7  cents,  and  Blake  4  cents  ;  they 
paid  all  their  money  for  22  apples  ;  how  many  ought 
each  to  receive  ? 

8.  Three  men  bought  a  lottery  ticket  for  $12  ;  the 
first  paid  $2,  the  second  $7,  and  the  third  $3.  They 
•drew  a  prize  of  $240  ;  what  was  each  man’s  share  ? 

9.  Three  men  hired  a  pasture  for  $24  ;  the  first  put 
in  2  horses,  the  second  put  in  3  horses,  and  the  third 
put  in  4  horses  ;  how  much  ought  each  to  pay  ? 

10.  A  man,  failing  in  business,  was  able  to  pay  only 
|  of  his  debts  ;  how  much  will  that  man  receive  to 
whom  lie  owes  $90  ? 

11.  A  man,  meeting  an  equal  number  of  poor  wo- 


PARTNERSHIP. 


115 


men  and  boys,  gave  to  each  woman  7  dimes,  and  to 
each  boy  2  dunes  ;  and  to  them  all  he  gave  $9  :  how 
many  women  and  boys  were  there  respectively  ?  * 

,12*  T^'°  111  en  bought  a  barrel  of  fish  for  $9  ;  the  first 

paid  *4,  the  second  $5  ;  what  part  of  the  barrel  belongs 
to  each  ? 

13.  A  farmer  gave  35  bushels  of  rye  to  two  of  his 
poor  neighbors ;  to  the  first  he  gave  1  bushel  as  often 
as  to  the  other  f  of  a  bushel :  how  many  bushels  did 

14.  Three  men  hired  a  pasture  for  $36  ;  the  first 
put  m  3  horses,  the  second  2  horses,  and  the  third  4 
Horses ;  how  much  ought  each  to  pay  ? 

*?•  T'P  men.  llired  a  Pasture  for  '$60  ;  the  first 
put  in  4  horses,  for  2  weeks,  and  the  second  put  in  3 

iS<f  ™  4  Weeks',  •  HoW  much  ought  each  to  pay  ? 

>.  three  men  hired  a  pasture  for  $15  ;  the  first 
put  m  4  sheep  for  5  weeks,  the  second  put  in  8  sheep 
foi  5  weeks,  and  the  third  put  in  10  sheep  for  9  weeks. 
How  much  ought  each  to  pay  ? 

nnD  J,T,VTo  entCTend  int0  Partnership;  the  first 
put  in  $40  .or  10  months  and  the  second  put  in  $80 

for  5  months ;  they  gained  $95  :  what  was  each  man’s 
snare  ot  the  gain  ? 

son8’  aA  agr,eed  t0  cut  a 'field  of  wheat  for 

'  A  3e.nt  5  men,  *  days,  and  B  sent  3  men  for 
10  days5.  how  much  ought  each  to  receive? 

19.  Divide  $56  between  A  and  B,  giving  to  A  $1 
as  often  as  to  B  f  of  a  dollar. 

20.  A  and  B  hired  a  pasture  for  $24 ;  A  put  in  4 
sheep  for  10  weeks,  and  B  put  in  2  horses  for  10 
weeks  ,  what  ought  each  to  pay  provided  2  sheep  in 
I  week  eat  as  much  as  a  horse  in  the  same  time  ? 

1.  bimpson,  Domer,  and  Ever  enter  into  a  joint 
speculation  by  which  they  clear  $460.  Simpson  claims 
to  nave  furnished  £  ;  Domer,  §;  and  Eyer,  \  of  the 
entire  capital.  IIow  much  according  to  these  Calcula¬ 
tions  ought  each  to  receive  ? 


116 


ALGEBRAIC  QUESTIONS. 


LESSON  IV. 

1.  B  had  4  apples  more  than  A,  and  they  together 
had  14;  how  many  had  each? 

Solution. — By  a  condition  of  the  question  B’s  number  is  equal 
to  A’s  +  4  apples ;  to  which  add  A’s  number,  and  we  have  2 
times  A’s  number  +  4=14.  Therefore,  2  times  A’s  number 
equals  14  —  4,  or  10;  and  once  his  number  equals  \  of  10,  or 
5  apples.  And  B’s  number  is  5 +4=9  apples. 

2.  Heman  has  6  books  more  than  Handford,  and 
both  have  26  ;  how  many  has  each  ? 

3.  Bobert  has  7  marbles  more  than  Richard,  and 
both  have  35  ;  how  many  has  each  ? 

4.  Mary  has  4  roses  more  than  Martha,  and  both 
have  24  ;  how  many  has  each? 

5.  Alice  has  7  pins  more  than  Abner,  and  both  have 
29  ;  how  many  has  each  ? 

6.  |  of  |  is  f  of  what  number  ? 

7.  The  sum  of  two  numbers  is  36,  and  their  differ¬ 
ence  is  16;  what  are  the  two  numbers  ? 

8.  A  boy  bought  4  of  a  melon  for  8-4  cents  ;  how 

much  is  that  a  piece  ? 

9.  Homer  and  Hannah  each  brought  an  equal  num¬ 
ber  of  peaches  ;  on  their  way  home  Hannah  had  4 
more  given  to  her,  then  they  together  had  24  ;  how 
many  did  each  buy  ? 

10.  Two  boys  had  each  an  equal  number  of  blocks  ; 
one  lost  4  of  his ;  and  together  they  then  had  only 
12  remaining  :  how  many  had  each  at  first  ? 

11.  A  wagon  was  sold  for  $17§,  which  was  §  as 
much  as  it  cost ;  what  did  it  cost  ? 

12.  Hiram  had  twice  as  many  strawberries  as 
Eugene,  and  both  had  18  pints  ;  how  many  had -each  ? 

13.  Ida  had  6  cents  more  than  twice  as  many  as 
Ira,  and  both  had  36  ;  how  many  had  each  ? 

14.  Susan  had  4  as  many  cents  as  Sarah  ;  Sarah 


ALGEBRAIC  QUESTIONS. 


117 


lost  10  of  hers  ;  then  together  they  had  50  ;  how- 
many  had  each  at  first? 

15.  Thomas  was  returning  from  market  with  twice 
as  many  eggs  as  Timothy  ;  Thomas  broke  4  of  his 
and  Timothy  6  of  his  ;  they  then  had  50  eggs  remain¬ 
ing.  How  many  had  each  at  first  ? 

16.  f  of  a  number  -f  14  =  44  ;  what  is  that 
number  ? 

17.  A  boy  being  asked  his  age,  replied,  3  times  my 
age  —  7  years  are  23  years.  How  old  was  he  ? 

18.  A,  being  asked  how  much  money  he  had,  re¬ 
plied,  twice  what  I  have  +  $60,  is  four  times  $400  ; 
how  much  money  had  A  ? 

19.  Two  boys  have  49  marbles,  but  the  first  has  7 
the  most ;  how  many  has  each  ? 

20.  A  man  bought  a  sheep,  a  cow,  and  a  horse  for 
$70  ;  the  cow  cost  $10  more  than  the  sheep,  and  the 
horse  cost  $20  more  than  the  cow.  What  was  the 
cost  of  each  ? 

21.  A  man  bought  a  melon  for  18f  cents,  which 
was  only  |  as  much  as  his  dinner  cost ;  what  was  the 
cost  of  his  dinner  ? 

22.  A  gentleman  bought  a  watch  and  chain  for  $80  ; 
the  chain  cost  i  as  much  as  the  watch  ;  what  was  the 
cost  of  each  ? 

23.  A  farmer  bought  a  plow,  a  harness,  and  a 
horse  for  $58  ;  for  the  harness  he  gave  $6  more  than 
for  the  plow,  and  for  the  horse  $34  more  than  for  the 
harness.  How  much  did  he  give  for  each  ? 

24.  A  boy  bought  twice  as  many  oranges  as  lemons, 
and  on  his  way  home  ate  4  oranges  and  gave  six  away  ; 
and  was  surprised  to  find  he  had  only  14  oranges  re¬ 
maining.  How  many  of  each  kind  did  he  buy  ? 

25.  5  times  a  certain  number  —  12  is  48  ;  what  is 
that  number? 

26.  -j  of  a  certain  number  —  5  is  40 ;  what  is  that 
number  ? 


118  ALGEBRAIC  QUESTIONS. 

27.  A  boy,  being  asked  bis  age,  replied,  11  years 
are  7  years  more  than  §  of  my  age  ;  how  old  was  he  ? 

28.  A  boy,  being  asked  how  many  sheep  his  father 
had,  replied,  40  are  5  less  than  £  of  his  number.  How 
many  had  he  ? 

29.  A  boy  bought  18  lemons  for  f  of  them  he 
paid  3  cents  for  2,  and  for  the  remainder  he  paid  3 
cents  a  piece  ;  for  what  must  he  sell  them  a  piece  to 
gain  10  cents  on  the  whole? 

30.  James,  John,  and  Joseph  together  have  96 
peaches  ;  James  has  2  more  than  John,  and  Joseph  has 
as  many  as  both  James  and  John  :  how  many  has  each  ? 

31.  Henry  bought  54  oranges;  for  §  of  them  he 
paid  2  cents  for  3,  and  for  the  remainder,  3  cents  for 
2 ;  and  sold  i  of  them,  at  the  rate  of  2  cents  for  3, 
and  the  remainder,  at  3  cents  for  2.  How  much  did 
he  gain  by  so  doing  ? 

— — — - — - 

■ 

LESSON  V. 

1.  If  a  man  can  do  a  certain  piece  of  work  in  12 
days,  what  part  of  it  can  he  do  in  1  day  ? 

2.  If  a  man  can  drink  a  barrel  of  beer  in  20  weeks, 
what  part  of  it  can  he  drink  in  1  week  ? 

3.  If  it  require  9  hours  to  empty  a  vessel,  what  part 
of  it  can  be  emptied  in  1  hour? 

4.  If  a  family  consume  a  barrel  of  pork  in  30  days, 
what  part  of  a  barrel  do  they  daily  consume  ? 

5.  If  it  require  19  days  to  perform  a  certain  jour¬ 
ney,  what  part  of  it  can  be  performed  in  1  day  ? 

6.  If  A  can  do  a  certain  piece  of  work  in  8  days, 
and  B  could  do  the  same  in  12  days ;  what  part  of  it 
can  each  do  in  a  day  ? 

7.  If  C  could  mow  a  certain  field  in  4  days,,  and  D 
could  do  the  same  in  6  days ;  what  part  of  it  could 


119 


ALGEBRAIC  QUESTIONS. 

each  do  in  a  day,  and  how  much  could  they  together 
do  *  x  a  day  ? 

J.  II  C  and  D  can,  in  1  day,  mow  ^  of  a  field,  how 
long  would  it  take  them  to  mow  the  whole  field  ? 

9.  How  many  days  would  it  take  to  perform  a  cer¬ 
tain  piece  of  work,  if  of  it  can  be  performed  in  1 
day  ? 

10.  If  George  can  do  a  certain  piece  of  work  in  3 
days,  and  Granvil  in  6  days ;  how  long  will  it  take 
them  together  to  do  the  work  ? 

11.  If  James  can  eat  a  bushel  of  apples  in  10  days, 
and  Rud  in  12  days;  how  long  would  1  bushel  last 
both  ? 

12.  A  can  cut  a  field  of- wheat  in  12  days,  and  B 
can  do  the  same  in  20  days  ;  how  long  would  it  take 
them  to  cut  the  field  when  they  work  together? 

13.  A  merchant  bought  a  hogshead  of  molasses  for 
$20,  10  gallons  of  which  leaked  out ;  how  must  he 
sell  the  remainder  a  gallon  to  gain  $6.50  ? 

14.  |  of  a  barrel  of  flour  cost  $4f,  what  -w  ill  f  of  a 
barrel  cost  ? 

15.  A  and  B  can  build  a  boat  in  20  days,  and  with 
the  assistance  of  G,  they  can  build  it  in  8  days.  JIow 
long  would  it  take  C  to  do  it  alone  ? 

16.  A  farmer  and  his  son  can  do  a  piece  of  work  in 
6  days  ;  the  son  can  do  the  same  in  27  days.  How 
long  would  it  take  the  father  to  do  the  work  ? 

17.  Three  pipes,  A,  B,  and  C  can  fill  a  cistern  in  2 
hours,  A  and  B  can  fill  it  in  4  hours,  and  A  and  C  can 
fill  it  in  3  hours.  How  long  would  it  take  each  to  fill  it  ? 

18.  If  a  barrel  of  beer  would  last  a  man  35  days, 
and,  the  man  and  his  son  20  days;  how  long  would  it 
last  the  son  alone  ? 

19.  A  box  of  tea,  usually,  lasted  a  man  and  his 
wife  9  months  ;  when  the  man  was  absent  it  would 
last  the  wife  12  months.  How  long  would  it  have 
lasted  the  man  alone  ? 


120 


ALGEBRAIC  QUESTIONS. 


20.  A,  B,  and  C  can  build  a  boat  in  20  days,  A  r  id 
B,  in  40  days,  and  A  and  C,  in  30  days.  How  lo  g 
would  it  take  each  separately  to  build  it  ? 

21.  Provided  A  could  drink  a  barrel  of  beer  in  24 
days,  and  B,  in  36  days ;  bow  long  would  it  take 
them  together  to  drink  a  barrel,  after  f  of  it  had 
leaked  out? 

22.  A  market-woman  bought  30  oranges,  and  had 
L  of  them  stolen ;  the  remainder  she  sold  at  3  cents 
each  and  thereby  gained  |  of  a  cent  on  each  orange 
bought.  How  much  did  they  cost  a  piece  ? 

23.  A  can  do  a  certain  piece  of  work  in  4^  days, 
and  A  and  B  together,  in  3  days.  After  A  did  ^  of 
the  work,  B  did  the  remainder  ;  how  long  did  it  take 
him  ? 

24.  If  A  can  do  a  certain  piece  of  work  in  f  of  a 
day,  how  much  can  he  do  in  1  day  ? 

25.  If  a  man  can  chop  a  cord  of  wood  in  |  of  a 
day,  how  much  can  he  chop  in  1  day  ? 

26.  Isaac  can  make  a  pair  of  boots  in  |  of  a  day, 
and  Ira  in  §  of  a  day  ;  how  many  pair  can  both  make 
in  1  day  ? 

21.  Samuel  can  cut  a  cord  of  wood  in  |  of  a  day, 
and  Theodore  in  §  of  a  day  ;  how  long  would  it  take 
them  to  cut  a  cord,  when  they  worked  together  ? 

28.  If  |  of  an  apple  cost  -f  of  a  cent,  what  will  f 
of  an  apple  cost? 

29.  A  can  mow  1  acre  of  grass  in  f  of  a  day,  B,  in 
|  of  a  day,  and  C,  in  j  of  a  day.  How  much  more 
can  A  and  B  mow  in  a  day  than  C  ? 

30.  If  a  wolf  can  eat  a  sheep  in  |  of  an  hour,  and 
a  bear  can  eat  it  in  f  of  an  hour,  how  long  would  it 
take  them  together  to  eat  what  remained  of  a  sheep 
after  the  wolf  had  been  eating  \  of  an  hour  ? 


i 


algebraic  questions. 


121 


LESSON  VI. 


1.  Lewis,  meeting  some  beggars,  gave  each  of  them 
2  cents,  and  had  12  cents  remaining ;  if  he  had  o-iven 
them  4  cents  each,  it  would  have  taken  all  the  money 
he  had.  How  many  beggars  were  there  ? 


bOLUTiON".  By  the  last  condition  of  the  question,  he  gave  each 
hag-gar  2  cents  more  than  by  the  first,  and  to  them  all,  12  cents 
m°i  e  than  by  the  first  condition.  Therefore  there  must  have 

been  been  as  many  beggars  as  2  is  contained  times  in  12,  which 
are  6  beggars.  ’ 


2.  A  boy  gave  to  each  of  his  playmates  3  cents,  and 
had  24.  cents  remaining ;  if  he  had  given  them  each  7 
cents,  it  would  have  taken  all  the  money  he  had. 
How  many  playmates  had  he  ? 

3.  Mary. gave  each  of  her  playmates  5  apples;  if 
she  had  given  them  each  7  apples,  it  would  have 
taken  1 2  apples  more.  How  many  playmates  had  she  ? 

4.  A  certain  number  ot  persons  gave  me  10  cents 
each  ;  had  they  given  me  12  cents  each,  it  would  have 
amounted  to  20  cents  more.  How  many  persons 
were  there  ? 

5..  |  of  $100  is  -gf  it  of  i  times  the  salary  of  the 
President  of  the  United  States.  What  is  his  salary  ? 

6.  $40  is  §  times  ¥V  of  the  salary  of  the  Vice  Presi¬ 
dent  of.  the  United  States.  What  is  his  salary  ? 

i.  Divide  35  oranges  between  James  and  Joseph,  so 
that  James  may  have  15  more  than  Joseph. 

8.  A  cask  of  wine  was  sold  for  $96,  which  was  -3  of 
twice  as  much  as  it  cost ;  how  much  did  it  cost  ?  4 

9.  By  selling  a  quantity  of  cotton  for  $560,  I  gained 
T  or  what  it  cost ;  how  much  did  it  cost  ? 

10.  A  and  B  are  187  miles  apart,  and  are  traveling 
towards  each  other ;  one  at  the  rate  of  8  miles  an  houi^ 
and  the  other,  9  miles  an  hour ;  how  many  hours  be¬ 
fore  they  will  meet  ? 


11 


122  ALGEBRAIC  QUESTIONS. 

11.  Agnes  gave  2  dimes  a  yard  for  a  piece  of  cali¬ 
co ;  liad  she  given  3  dimes  a  yard,  it  would  have  cost 
her  20  dimes  more  ;  how  many  yards  did  the  piece 
contain  ? 

12.  A  was  ordered  to .  buy  a  certain  number  of 
oranges  ;  if  he  bought  those,  at  2  cents  each,  he  would 
have  had  no  money  left, — had  he  bought  those,  at  3 
cents  each,  he  would  have  wanted  10  cents  more  to 
have  paid  for  them.  How  many  oranges  was  he  re¬ 
quired  to  buy  ? 

13.  A  lady  wished  to  buy  a  certain  number  of  yards 
of  muslin  ;  there  were  two  kinds,  some  at  9  cents  a 
yard,  and  some  at  12  cents  a  yard.  Had  she  taken 
that  at  12  cents  a  yard,  it  would  have  cost  36  cents 
more  than  the  other  kind.  How  many  yards  did  she 
wish  to  buy  ? 

14.  A  boy  being  sent  to  market  to  buy  a  certain 
number  of  pounds  of  meat,  found,  if  he  bought  beef, 
at  5  cents  a  pound,  he  would  have  39  cents  remaining, 
but  if  he  bought  pork,  at  8  cents  a  pound,  he  would 
have  only  6  cents  remaining.  For  how  much  meat 
was  he  sent  ? 

15.  If  8  times  a  certain  number,  is  36  more  than  5 
times  the  same  number,  what  is  that  number  ? 

16.  A  boy  being  asked  his  age,  said,  4  times  my  age 
is  24  years  more  than  2  times  my  age  ;  how  old  was  he? 

17.  A  boy,  being  asked  how  many  sheets  of  paper 
he  had,  said,  4  times  the  number,  is  1 8  less  than  7 
times  the  number  ;  how  many  sheets  of  paper  had  he  ? 

18.  A  person,  wishing  to  buy  some  butter,  found,  if 
he  bought  that  which  was  10  cents  a  pound,  he  would 
have  20  cents  remaining ;  but  if  he  bought  that  which 
was  12  cents  a  pound,  he  would  lack  14  cents  of  hav¬ 
ing  money  enough  to  pay  for  it.  How  many  pounds 
did  he  wish  to  buy  ? 

19.  A  farmer,  wishing  to  buy  a  certain  number  of 
sheep,  found  if  he  gave  $2  a  head,  he  would  have  $20 


ALGEBRAIC  QUESTIONS.  123 

remaining ;  but  if  he  gave  $5  a  head  he  would  lack 
$40  of  having  money  enough  to  pay  for  them.  How 
many  sheep  did  he  wish  to  buy  ? 

20.  A,  B,  and  C,  talking  of  their  ages  ;  says  A  to  B, 
I  am  4  times  as  old  as  you ;  says  B  to  C,  I  am  |  as 
old  as  you,  but  says  A  to  C,  I  am  40  years  older  than 
you.  Required  the  age  of  each  ? 

LESSON  V I L 

1.  A  laborer  agreed  to  work  40  days  upon  this  con¬ 
dition  ;  that  for  every  day  he  worked,  he  should 
receive  $2,  and  for  every  day  he  was  idle  he  should 
pay  $1  for  his  board.  At  the  expiration  of  the  time, 
he  received  $50.  How  many  days  did  he  work  ? 

Solution. — If  he  had  labored  the  whole  time,  he  would  have 
received  40  times  $2,  or  $80.  But  he  received  only  $50 :  he, 
therefore,  lost  by  his  idleness  $80  —  $50,  or  $30.  For  every 
day  he  was  idle  he  lost  $2  (his  daily  wages)  +  $1  (the  cost  of 
his  board)  which  are  $3.  If  in  1  day  he  lose  $3  ;  he  will  lose 
$1  in  4  of  a  day,  and  $30  in  30  times  4  of  a  day,  or  10  days. 
Therefore,  he  was  idle  10  days,  and  worked  40  —  10  days,  or 
30  days. 

2.  A  man  agreed  to  work  60  days  on  this  condi¬ 
tion  ;  that  for  every  day  he  worked  he  should  receive 
$li,  and  for  everyday  he  was  idle,  he  should  pay  If- 
for  his  board.  At  the  expiration  of  the  time,  he  re¬ 
ceived  $68.  How  many  days  did  he  work  ? 

3.  A  man  wras  hired  for  80  days,  on  this  condition; 
that  for  every  day  he  worked,  he  should  receive  6 
dimes,  and  for  every  day  he  was  idle,  he  should  forfeit 
4  dimes.  At  the  expiration  of  the  time,  he  received 
$40.  How  many  days  did  he  work  ? 

4.  How  many  times  §  of  12  is  £  of  48  ? 

5.  A  and  B  bought  a  quantity  of  flour  for  $50;  A 
paid  $1  as  often  as  B  |  of  a  dollar;  what  part  of  the 
flour  belongs  to  each  % 


124  algebraic  questions. 

6.  A,  B,  and  C  built  a  house,  -which  cost  $500,  of 
-which  B  paid  $100  more  than  A,  and  C  paid  as  much 
as  A  and  B  both  ;  how  much  did  each  pay  ? 

*7.  A  merchant  sold  a  quantity  of  cloth  for  $84,  and 
thereby  lost  f  of  what  it  cost ;  what  did  it  cost  ? 

8.  7|  is  2i  times  f  of  how  many  times  li  ? 

9.  A  farmer  having  in  his  employ  an  equal  number 
of  men  and  boys ;  to  each  boy  he  gave  $4,  to  each 
man  $8 ;  and  to  them  all  he  gave  $84  :  how  many 
men  were  there  ? 

10.  Two  men  hired  a  pasture  for  $35  ;  one  put  in  3 
cows,  and  the  other  put  in  4  ;  how  much  ought  each 
to  pay  ? 

11.  A  man  sold  an  equal  number  of  ducks  and 
turkeys  for  20  dimes  ;  the  ducks,  at  2  dimes  each,  and 
the  turkeys,  at  3  dimes  each  ;  how  many  did  he  sell 
in  all? 

12.  A  farmer  sold  an  equal  number  of  ducks  and 
turkeys  ;  the  ducks,  at  4  dimes  eacn,  the  turkeys,  at 
7  dimes  each  ;  and  for  the  turkeys  he  received  $3 
more  than  for  the  ducks  ;  how  many  of  each  kind  did 
he  sell  ? 

13.  There  are  two  baskets,  containing  37  apples; 
in  one  of  which  there  are  17  more  than  in  the  other; 
how  many  apples  are  there  in  each  ? 

14.  Charles  and  Henry  together  have  49  marbles, 
and  Charles  has  7  more  than  twice  as  many  as  Henry  : 
how  many  has  each  ? 

15.  Philip  has  20  apples  more  than  Philo  ;  and  to¬ 
gether  they  have  92  ;  how  many  has  each  ? 

16.  Three  boys  have  47  lemons;  the  first  has  3 
more  than  the  second,  and  the  second  has  7  more 
than  the  third  ;  how  many  has  each  ? 

17.  A  boy  was  hired  for  20  days,  on  this  con¬ 
dition  ;  that  for  every  day  he  labored,  he  should  re¬ 
ceive  3  dimes,  and  for  every  day  he  was  idle,  he 
should  pay  2  dimes  for  his  board.  At  the  expiration 


ALGEBRAIC  QUESTIONS. 


125 


»  of  the  time  he  received  only  $1.  How  many  days 
was  he  idle  ? 

18.  A  boy  bought  a  whistle,  a  whip,  and  a  drum 
for  *70  cents.  For  the  whip  he  gave  twice  as  much  as 
for  the  drum,  and  for  the  drum,  twice  as  much  as  for 
the  whistle  ;  how  much  did  he  give  for  each  ? 

19.  The  sum  of  three  numbers  is  54.  The  first  is 
twice,  and  the  third  3  times  the  second  ;  what  are 
those  numbers? 

20.  Sarah’s  age  is  §  of  Susan’s,  and  the  sum  of  their 
ages  is  24  ;  what  is  the  age  of  each? 

21.  f  of  an  army  were  killed,  f  of  the  remainder 
»  taken  prisoners,  and  400  escaped.  How  many  were 

there  in  the  army  ? 


• - - — ■<-*«  »  » •*-  •>- - - 

LESSON  VIII. 

1.  A  fishing  rod,  the  length  of  which  was  14  feet, 
was  broken  into  two  pieces.  The  shorter  piece  was  £ 
of  the  length  of  the  longer.  What  was  the  length  of 
each  piece  ? 

Solution.-—!  of  the  length  of  the  longer  piece,  which  is  the 
length  of  the  shorter,  +  £,  (the  length  of  the  longer)  =J  of  the 
length  of  the  longer,  which  is  the  length  of  both,  or  14  feet. 
If  £  of  the  longer  is  14  feet,  J-  is  4  of  14  feet,  which  is  2  feet, 
and  £  (which  is  the  length  of  the  longer)  are  4  times  2  feet,  or  8 
feet.  14 — 8  =  6  feet,  the  length  of  the  shorter  piece. 

2.  A  pole,  tlie  length,  of  which  is  20  feet,  is  in  the 
air  and  water,  of  the  length  in  the  air  equals  the 
length  in  the  water  ;  what  is  the  length  in  the  air  and 
water  respectively  ? 

3.  If  in  2  days  a  man  traveled  160  miles,  and  f  of 
the  distance  he  traveled  the  first  day,  equals  the  dis¬ 
tance  he  traveled  the  second  day  ;  how  far  did  he 
travel  each  day  ? 


11* 


126 


ALGEBRAIC  QUESTIONS. 


4.  B  and  C  together  have  40  marbles ;  how  many 
has  each,  provided  f  of  B’s  number  is  equal  to  C’s  ? 

5.  From  New  York  City  to  Redhook  is  100  miles, 
and  i  of  the  distance  from  New  York  to  Rhinebeck, 
equals  the  distance  from  Rhinebeck  to  Redhook.  How 
far  from  Rhinebeck  to  New  York,  and  how  far  from 
Rhinebeck  to  Redhook  ? 

6.  If  a  horse  and  a  colt  were  worth  $90,  and  the 
horse  was  worth  H  times  as  much  as  the  colt;  what 
was  the  value  of  each  ? 

7.  A  boy  paid  70  cents  for  a  slate  and  a  book ;  how 
much  did  he  pay  for  each,  provided  the  book  cost  1£ 
times  as  much  as  the  slate  ? 

8.  If  a  traveler  pay  $1.20  for  his  breakfast  and 
dinner ;  how  much  did  he  pay  for  each,  provided 
his  dinner  cost  f  as  much  as  his  breakfast  ? 

9.  A  pole,  the  length  of  which  is  67  feet,  is  in  the 
air  and  water ;  §  of  the  length  in  the  air  +  7  feet 
equals  the  length  in  the  water.  Required  the  length 
in  the  air,  and  in  the  water  ? 

10.  Divide  the  number  108  into  two  such  parts, 
that  j  of  the  first  -f-  8  shall  equal  the  second. 

11.  Divide  the  number  97  into  two  such  parts,  that 
£  of  the  first  +  7  shall  equal  the  second? 

12.  There  is  a  fish  the  length  of  which  is  18  feet; 
its  tail  is  4  feet,  and  §  the  length  of  the  body,  equals 
the  length  of  the  head.  What  is  the  length  of  the 
head  and  body  respectively  ? 

13.  There  is  a  fish  the  weight  of  which  is  11 
pounds,  and  i  of  the  weight  of  the  head  +  8  pounds 
equals  the  weight  of  the  body  ;  what  is  the  weight  of 
each  ? 

14.  A  sliip-mast  51  feet  in  length,  was  broken  off 
in  a  storm,  and  §  of  the  length  broken  off,  equaled  £ 
of  the  length  remaining ;  how  much  was  broken  off, 
and  how  much  remained  ? 

15.  A  boy  being  asked  how  many  apples  and 


ALGEBRAIC  QUESTIONS. 


127 


oranges  he  had,  answered,  in  all  I  have  36,  and,  §  of 
the  number  of  apples,  equals  \  ot  the  number  ol 
oranges  ;  how  many  of  each  hind  had  lie^ 

lgb  2  0f  one  number  equals  f  ot  another,  and  their 

sum  is  57  ;  what  are  the  two  numbers  ? 

17.  A  farmer  has  290  sheep  in  two  different  fields; 
and  £  of  the  number  in  the  first  field,  equals  f  of  the 
number  in  the  second ;  how  many  are  there  in  each 

field? 

18.  A  market  woman  was  requested  to  buy  33 
fowls,  consisting  of  two  kinds ;  £  of  the  number  of  the 
first  kind,  was  to  equal  §  of  the  number  ot  the  second  ; 
how  many  of  each  kind  must  she  buy  ? 

19.  A  person,  being  asked  the  time  of  day,  said,  the 
time  past  noon  is  £  of  the  time  past  midnight ;  what 
was  the  hour  ? 

Remark. — Since  the  time  past  noon  is  1  of  the  time  past 
midnight,  the  time  from  midnight  to  noon,  which  is  12  hours, 
must  be  £  ot  the  time  past  midnight. 

20.  A  person,  being  asked  the  hour  of  the  day,  said, 
the  time  past  noon,  is  £  of  the  time  past  midnight ; 

what  was  the  hour  ?  . , 

21.  A  person,  being  asked  the  hour  of  the  day,  said, 
the  time  past  noon,  is  £  of  the  time  from  now  to  mid¬ 
night  \  what  is  the  hour  ? 

Solution. — From  now  to  midnight  is  §,  and  l  added  (the  time 
past  noon)  is  \ .  Consequently  from  noon  to  midnight  (winch  is 
12  hours)  is  £  of  the  time  it  lacked  of  being  midnight;  and  ‘  ot 
the  time,  is  £  of  12,  which  is  3  hours,  the  time  past  noon. 

22.  What  is  the  time  of  day,  provided  £  of  the  time 
from  now  to  midnight  equals  the  time  past  noon  ? 

23.  A  man,  being  asked  the  hour  of  the  day,  said, 
|  of  the  time  past  noon,  equals  f  of  the  time  from  now 
to  midnight ;  what  was  the  time  ? 

24.  A  pole  the  length  of  which  was  ^  68  feet  was  m 
the  air  and  water ;  £  of  the  length  in  the  air,  equaled 


1 1 


128 


ALGEBRAIC  QUESTIONS. 


|  of  the  length  in  the  water.  What  was  the  length  in 
the  air,  and  in  the  water  respectively  ? 

25.  The  sum  of  two  numbers  is  1 T6,  and  f  of  the 
first  +  4 .  equals  §  of  the  second  ;  required  the  numbers  ? 

26.  A  person,  being  asked  the  time  of  day,  said,  ■} 
of  the  time  past  midnight  equals  T3F  of  the  time  from 
now  to  midnight  again  ;  what  o’clock  is  it  ? 

27.  Provided  the  time  past  10  o’clock,  A.  M.,  equals 
f  of  the  time  to  midnight ;  what  o’clock  is  it  ? 

28.  Says  A  to  B,  f  of  my  age  +  4  years  equals  | 
of  yours,  and  the  sum  of  our  ages  is  74  years.  What 
is  each  of  their  ages  ? 

29.  A  person,  being  asked  the  hour  of  the  day,  re¬ 
plied,  |  of  the  time  past  noon,  equals  |  of  the  time 
from  now  to  midnight  +  2§  hours  ;  what  was  the  time  ? 

30.  A  pole,  the  length  of  which  is  78  feet,  is  in  the 
air  and  water  ;  f  of  the  length  in  the  air  +12  feet, 
equals  times  the  length  in  the  water.  What  is  the 
length  in  the  air  and  water  respectively  ? 

- ».♦■»  - 

LESSON  IX. 

1.  There  is  a  fish  the  head  of  which  is  4  inches 
long,  and  whose  tail  is  as  long  as  its  head  +  \  of  its 
body,  and  whose  body  is  as  long  as  its  head  and  tail ; 
what  is  the  length  of  the  fish  ? 

Solution. — By  a  condition  of  the  question,  £  of  the  length 
of  body  +  4  inches,  is  the  length  of  tail ;  to  which  add  4 
inches,  (the  length  of  the  head),  and  we  have  i  of  the  length  of 
the  body  +  8  inches  =  or  the  length  of  the  body.  There¬ 
fore,  -f  —  or  ^  of  the  length  of  the  body,  equals  8  inches ;  and 
f,  or  twice  the  length  of  the  body,  which  is  the  length  of  the 
fish,  equals  4  times  8  inches,  or  32  inches. 

2.  The  head  of  a  fish  is  6  inches  long,  its  tail  is  as 
long  as  its  head  +  \  of  its  body,  and  the  body  is  as 


ALGEBRAIC  QUESTIONS.  129 

long  as  the  head  and  tail  together ;  what  is  the  length 
of  the  fish  ? 

3.  The  head  of  a  fish  is  12  inches  long,  the  tail  is  as 
long  as  the  head  +  |  of  the  body,  and  the  body  is  as 
long  as  the  head  and  tail ;  what  is  the  length  of  the 
fish  ? 

4.  The  head  of  a  fish  weighs  10  pounds,  the  tail 
weighs  as  much  as  the  head  + 1-  as  much  as  the  body  5 
and  the  body  weighs  as  much  as  the  head  and  tail ; 
wThat  is  the  weight  of  the  tail  ? 

5.  -f  of  a  certain  number  equals  f  of  the  same  num¬ 
ber  +  10  ;  what  is  that  number  ? 

G.  A  boy,  being  asked  his  age,  replied,  f  of  my 
age  exceeded  of  my  age  by  4  years  ;  how  old  was 
he  ? 

V.  James,  being  asked  how  many  arithmetical  ques¬ 
tions  he  had  answered  correctly  during  the  week,  re¬ 
plied,  f  of  the  number  is  3  more  than  f  of  the  num¬ 
ber*,  how  many  questions  had  he  answered  ? 

8.  A  farmer  after  selling  §•  of  1-|  times  as  much 
grain  as  he  had,  had  80  bushels  remaining  ;  how  much 
had  he  at  first  ? 

9.  An  individual,  after  spending  f  of  all  his  money, 
and  |  of  what  then  remained,  had  only  $12|  remain¬ 
ing  ;  how  much  had  he  at  first  ? 

"lO.  If  4  of  a  ship  be  worth  f  of  her  cargo  which 
is  valued  at  300  eagles  ;  what  is  the  value  of  the 
ship  ? 

11.  Dick  being  asked  how  much  money  he  had, 
said,  its  \  exceeded  its  f  by  $2  ;  how  much  had  lie? 

12.  A  tree  by  falling,  was  broken  into  three  pieces; 
the  top  part  was  10  feet  long,  the  bottom  part  was  as 
long  as  the  top  -f  f  of  the  middle,  and  the  middle 
part  was  as  long  as  the  other  two;  what  was  the  length 
of  the  tree,  and  of  each  piece  ? 

13.  A  man  bought  a  hat,  a  coat,  and  a  watch ;  the  hat 
cost  $6,  the  watch  cost  as  much  as  the  hat  +  §  of  the 


130  ALGEBRAIC  QUESTIONS. 

cost  of  the  coat,  and  the  coat  cost  as  much  as  the  hat 
and  watch  ;  what  was  the  cost  of  each,  and  of  all  ? 

14.  |  of  f  is  how  many  times  §  of  T5¥  ? 

15.  If  f  of  a  ton  of  hay  cost  f  of  an  eagle,  how 
many  dollars  will  \  of  a  ton  cost? 

16.  A  third  and  \  of  a  third  of  10  is  f  of  what 
number  ? 

17.  If  from  a  certain  number  you  take  its  |  and  its 
i,  the  remainder  will  he  13|,  what  is  that  number  ? 

18.  After  spending  §  of  my  money,  I  earned  f  as 
much  as  I  spent,  and  then  had  only  $20  less  than  what 
I  had  at  first ;  how  much  had  I  at  first  ? 

19.  The  head  of  a  fish  is  8  inches  long,  the  tail  is 
as  long  as  the  head  and  \  of  the  body  +  10  inches, 
and  the  body  is  as  long  as  the  head  and  tail ;  what  is 
the  length  of  the  fish  ? 

20.  The  head  of  a  fish  is  12  inches  long ;  its  tail  is 
10  inches  longer  than  its  head  increased  by  |  the  length 
of  the  body  ;  and  its  body  is  20  inches  longer  than  its 
head  and  tail  together.  What  is  the  length  of  the  fish  ? 

- - <  'i  »  i'  - 

LESSON  X. 

1.  James  is  20  years  old,  and  John  is  4  years  old, 
in  how  many  years  will  James,  who  is  now  5  times  as 
old  as  John,  be  only  twice  as  old  ? 

Remark.— Four  years  ago  James  was  16,  and  in  16  years 
more  he  will  be  twice  as  old  as  John. 

2.  Sarah  is  10  years  old,  and  Sally  is  4  ;  in  how 
many  years  will  Sally  be  -i  as  old  as  Sarah  ? 

3.  Jacob  is  40  years  old,  and  Alfred  is  2  ;  in  how 
many  years  will  Alfred  be  \  as  old  as  Jacob  ? 

4.  If  the  third  of  6  be  3,  what  will  b  of  20  be  ? 

5.  If  3  be  the  third  of  6,  what  will  the  }  of  20  be  ? 

6.  If  |  of  12  be  10,  what  will  §  of  10  be? 


ALGEBRAIC  QUESTIONS.  131 

Y.  Divide  the  number  85  into  two  parts,  that  shall 
be  to  each  other  as  §  to  £. 

8.  When  A  was  married,  he  was  3  times  as  old  as 
his  wife,  but  when  they  had  been  married  15  years,  he 
was  only  twice  as  old  as  she ;  how  old  was  each  when 
they  were  married  ? 

Remark. — The  conditions  of  the  above  question  give  the  fol¬ 
lowing  : 

9.  Three  times  a  certain  number  +15  equals  twice 
the  same  number  +  30  ;  what  is  that  number,  and 
what  is  3  times  the  same  number  ? 

10.  Once  a  certain  number  +  15  equals  §  of  the 
same  number  +  30  ;  what  is  that  number,  and  what 
is  i  of  the  same  number  ? 

11.  When  I  first  met  Mr.  A,  I  was  \  as  old  as  he 
was,  and  in  12  years  after  that,  I  was  f  as  old  as  he 
was;  what  was  each  of  our  ages  when  we  first  met  ? 

12.  There  are  two  numbers,  one  of  which  is  4  times 
the  other;  but  if  to  each  20  were  added,  one  will  be 
double  the  other;  wha*  are  these  numbers  ? 

13.  When  B  was  married  he  was  3  times  as  old  as 
his  wife ;  but  after  they  had  been  married  60  years, 
|  of  his  age  equaled  hers  ;  what  was  the  age  of  each 
when  they  were  married  ? 

14.  A  hound  takes  3  leaps  to  a  fox  4,  and  3  of  the 
hound’s  leaps  are  equal  to  6  of  the  fox’s  ;  how  many 
leaps  must  the  hound  take  to  gain  1  on  the  fox  ? 

15.  If  the  hound  takes  leaps  to  gain  1,  on  the 
fox ;  how  many  must  he  take  to  gain  20  on  the  fox  ? 

16.  A  hare  is  20  leaps  before  a  hound,  and  takes  4 
leaps  to  the  hound  3  ;  and  3  of  the  hound’s  leaps  are 
equal  to  6  of  the  hare’s.  How  many  leaps  must  the 
hou^d  take  to  catch  the  hare  ? 

1/.  A  fox  is  60  leaps  before  a  hound,  and  takes  5 
leaps  tc  the  hound  2  ;  and  4  of  the  hound’s  leaps 
equals  12  of  the  fox’s.  How  many  leaps  must  the 
hound  take  to  catch  the  fox  ? 


132 


ALGEBUAIC  QUESTIONS. 


18.  Alfred  is  60  steps  before  Silas,  and  takes  9  steps 
to  Silas  0  ;  and  3  of  Silas’s  steps  equals  7  of  Alfred’s. 
IIow  many  steps,  at  this  rate,  will  each  take  before 
they  will  be  together  ? 

Remark. — A  box  of  glass  contains  50  square  feet ,  or  as  nearly 
as  may  be. 

19.  How  many  panes  of  glass  in  a  box,  provided 
they  are  6,  by  8  inches  ? 

Remark. — Find  the  area  of  a  pane  of  glass  by  reducing  the 
inches  to  parts  of  a  foot,  and  then  multiply  these  parts  together. 
The  area  of  a  pane  G  by  8  inches  is  4  of  a  square  foot.  The  re¬ 
mainder  may  be  solved  as  follows : 

Solution. — If  to  make  |  of  a  square  foot  it  require  1  pane, 
to  make  §,  or  1  square  foot,  it  will  require  3  times  1,  or  3  panes; 
and  to  make  50  square  feet  (1  box,)  it  will  require  50  times  3 
panes,  which  are  150  panes. 

20.  IIow  many  panes  of  glass  in  a  box,  provided 
they  are  8,  by  10  inches? 

21.  How  many  panes  of  glass  in  a  box,  provided 
they  are  10,  by  12  inches? 

22.  How  many  panes  of  glass  in  a  box,  provided 
they  are  8,  by  12  inches? 

23.  How  many  panes  of  glass  in  a  box,  provided 
they  are  12  by  15  inches? 


LESSON  XL 

* 

1.  What  number  is  that,  to  which  if  its  a  be  added, 
the  sum  will  be  1 5  ? 

2.  What  number  is  that,  to  which  if  its  A  be  added, 
the  sum  will  be  24  ? 

3.  Wh&t  number  is  that,  to  wdiich  if  its  a  be  added, 
the  sum  will  be  40  ? 

4.  What  number  is  that,  to  which  if  its  a  bf  t.dded, 
the  sum  will  be  30  ? 

5.  What  number  is  that,  to  which  if  its  §  be  added, 
the  sum  will  be  88  ? 


ALGEBRAIC  QUESTIONS. 


133 


6.  How  old  is  that  man,  to  whose  age  if  you  add 
its  i  and  its  §,  the  sum  will  be  104  years? 

V.  What  number  is  that,  which  being  increased  by 
its  J,  its  i  and  18  more  will  be  doubled? 

8.  A  man,  being  asked  his  age,  said,  my  age^  in¬ 
creased  by  its  f  and  20  more,  is  double  my  age.  What 
was  his  age  ? 

9.  Suppose  I  buy  a  certain  number  of  boxes  of  but¬ 
ter,  at  $2  a  box,  and  as  many  more  at  $4  a  box  ;  and 
sell  them  all,  at  $3  a  box ;  do  I  gain  or  lose,  and  how 
much  ? 

10.  A  boy,  being  asked  how  many  oranges  lie  had, 
replied,  if  my  number  were  increased  by  its  f,  its  f, 
and  42  more,  the  sum  would  equal  3  times  my  num¬ 
ber.  How  many  had  he  ? 

11.  Suppose  I  buy  a  certain  number  of  melons  5 
some  at  10  cents  each,  and  as  many  more  at  40  cents 
each  ]  and  sell  them  all,  at  30  cents  apiece  *,  Iioav 
much  do  I  gain  on  each  melon  ? 

12.  If  by  selling  1  apple  I  lose  ot  a  cent,  how 
many  apples,  at  this  rate,  must  I  sell  to  lose  6  cents  ? 

13.  A  boy  bought  a  certain  number  of  lemons,  at  2 
cents  apiece,  and  as  many  more,  at  4  cents  apiece  ; 
and  sold  them,  at  the  rate  of  3  for  5  cents  :  did  he 
gain  or  lose,  and  how  much? 

14.  A  woman  bought  a  certain  number  ot  apples, 
at  the  rate  of  2  for  a  cent,  as  many  more,  at  the  rate 
of  3  for  a  cent  ',  and  sold  them  all,  at  the  rate  ot  5  for 
2  cents,  and  by  so  doing,  lost  4  cents.  How  many  of 
each  kind  did  she  buy  ? 

15.  A  woman  bought  a  certain  number  of  eggs,  at 
the  rate  of  3  for  a  cent,  and  as  many  more,  at  4  for  a 
cent ;  and  sold  them  out,  at  the  rate  ot  8  for  3  cents, 
and  by  so  doing,  gained  4  cents.  How  many  eggs  did 
she  buy  ? 

16.  Three  men  agreed  to  share  $510  in  the  propor¬ 
tion  of  h  h  and  1  ;  how  much  must  each  receive  ? 

12 


134 


ALGEBRAIC  QUESTIONS. 


17.  A’s  fortune  is  to  B’s  as  ^  to  i  ;  and  they  to¬ 
gether  have  1 100  ;  how  much  has  each  ? 

18.  The  difference  of  two  numbers  is  15,  which  is 
|  of  twice  as  much  as  the  smaller  number ;  what  are 
these  two  numbers  ? 

19.  A  merchant  bought  a  certain  number  of  yards 
of  cloth,  at  the  rate  of  2  yards  for  $1,  and  as  many 
more,  at  the  rate  of  5,  for  $1  ;  and  sold  them  all,  at 
the  rate  of  10  yards  for  $3  ;  and  thereby  lost  $8. 
How  many  yards  did  he  buy  ? 

20.  A  man  bought  a  certain  number  of  melons,  at 
the  rate  of  4  for  $1,  and  as  many  more,  at  the  rate  of 
10  for  $1  ;  and  sold  them  all,  at  the  rate  of  8  for  $2, 
and  thereby  gained  $6.  How  many  melons  did  he 
buy  ? 

- ■*-•>  - 

LESSON  XII. 

1.  Mary  has  twice  as  many  apples  as  Sarah,  and 
they  together  have  12  ;  how  many  has  each  ? 

Remark. — By  the  condition  of  the  question  Mary  has  2  apples 
as  often  as  Sarah  1.  Consequently  Mary  must  have  and 
Sarah  £  of  the  12  apples. 

2.  Divide  18  into  2  such  parts,  that  one  shall  be 
twice  the  other? 

3.  Divide  21  oranges  between  two  boys,  so  that  one 
may  have  twice  as  many  as  the  other. 

4.  Franklin  and  Francis  together  have  15  quarts 
of  nuts,  but  Franklin  has  twice  as  many  as  Francis ; 
how  many  has  each  ? 

5.  Robert  has  twice  as  many  cents  as  Harry,  and 
together  they  have  24  ;  how  many  has  each  ? 

6.  Divide  the  number  27  into  two  parts,  that  shall 
be  to  each  other  as  1  to  2. 

7.  Harriet  is  twice  as  old  as  Ellen,  and  the  sum  of 
their  ages  in  30  years  ;  what  is  the  age  of  each  ? 

8.  A  and  B  are  36  rods  apart,  and  travel  towards 


ALGEBRAIC  QUESTIONS, 


135 


eacli  other  ;  how  far  will  each  travel^before  they  meet, 

provided  A  travels  twice  as  fast  as  B  ?  _  e 

9.  What  number  must  be  added  to  twice  itseit,  tiiat 

the  sum  may  be  57  ?  .  ,  „  •- 

10.  A,  after  spending  ‘  of  all  his  money,  and  ^  ot 

the  remainder  less  $4,  had  only  $14  remaining  ;  how 

much  had  be  at  first  ?  <  , 

11.  Divide  the  number  48  into  two  such  parts,  that 

one  shall  be  f  of  the  other. 

19  In  a  certain  school,  there  are  3  times  as  many 
boys' as  girls,  and  in  all  there  are  62  pupils ;  how 
many  boys  and  how  many  girls  in  the  schoo 

13.  James  and  Jackson  together  have  45  marbles, 
but  James  has  only  |  as  many  as  Jackson  ;  how  many 

T~|  0^0]l  \  , 

14  A  man  and  his  son  together  earned  $280  m  a 
year :,  how  much  does  each  earn,  provided  the  boy 

earns  only  i  as  much  as  his  fathei  ? 

15.  A  boy  bought  a  melon  and  a  citron  101  $1  , 
how  much  did  each  cost,  provided  the  melon  cost  only 

\  as  much  as  the  citron  ?  ,  . 

16.  A  man  bought  a  horse  and  a  saddle  ioi  $120  , 

the  saddle  cost  only  \  as  much  as  the  horse ;  what 
was  the  cost  of  each  ? 

17.  A  man,  being  ashed  the  cost  of  his  oxen,  said, 
my  oxen  and  wagon  together  cost  $240,  and  the  oxen 
cost  twice  as  much  as  the  wagon ;  what  was  the  cost 

18.  A  man  bought  a  sheep,  a  hog,  and  cow  for  $42  , 
for  the  hog,  he  gave  twice  as  much  as  for  the  sheep, 
and  for  the  cow,  3  times  as  much  as  for  the  sheep. 

How  much  did  he  give  lor  each  ?  .  1 

19.  A  farmer  and  his  two  sons  earned  $560  m  1 
year  ;  the  father  earned  twice  as  much  as  his  elder  son, 
and  the  elder  son  earned  twice  as  much  as  the  younger 

son.  How  much  did  each  earn  \ 

20.  A,  B,  and  C  together,  in  1  day,  can  dig  10a 


136  ALGEBRAIC  QUESTIONS. 

bushels  of  potatoes  ;  A  digs  \  as  much  as  B,  and  B,  ± 
as  much  as  C.  How  many  bushels  can  each  dig  in  a 
day  ? 

21.  A  man  bought  three  pieces  of  cloth  for  $160  ; 
the  first  piece  cost  only  i  as  much  as  the  second,  and 
the  second,  only  t  as  much  as  the  third.  IIow  much 
did  each  piece  cost? 

22.  In  an  army  consisting  of  20,000  men ;  3  times 
as  many  were  wounded  as  were  killed,  and  4  times 
as  many  remained  unhurt  as  were  wounded.  How 
many  were  killed,  wounded,  and  unhurt  respect¬ 
ively  ? 

23.  i  of  A’s,  +  f  of  B’s  money  equals  $5500  ;  and 
f-  of  B’s  money  is  4  times  of  A’s.  How  much 
money  has  each  ? 

24.  Herman  and  Byron  together  have  60  blocks ; 
and  Byron  owns  |  as  many  as  Herman ;  how  many 
has  each  ? 

25.  Divide  the  number  60  into  two  parts,  that  shall 
be  to  each  other  as  \  to  f  ? 

26.  Adelia  and  Louisa  arc  to  share  14  apples  in 
the  proportion  of  4  to  3  ;  how  many  ought  each  to 
receive  ? 

27.  The  sum  of  Mary  and  Hezekiah’s  age  is  25 
years  ;  how  old  is  each,  provided  Hezekiah  is  only  § 
as  old  as  Mary  ? 

28.  Henry  and  his  father  can  thrash  35  bushels  of 
oats  in  a  day  ;  how  many  does  each  thrash,  if  Henry 
thrashes  only  |  as  much  as  his  father  ? 

29.  A  pole,  whose  length  is  70  feet,  is  in  the  air 
and  water  ;  how  much  is  in  the  air  and  water  respect¬ 
ively,  if  |  of  the  length  in  the  air  equals  the  length  in 
the  water  ? 

30.  Divide  the  number  36  into  two  parts,  that  shall 
be  to  each  other  as  5  to  4. 

31.  Divide  the  number  45  into  two  parts,  that  shall 
be  to  each  other  as  1  to  f . 


ALGEBRAIC  QUESTIONS.  137 

32.  A  and  B  together  own  $480 ;  but  A  owns  only 
|  as  much  as  B  ;  how  much  belongs  to  each? 

33.  A  man  died,  and  left  $7200  to  be  divided  be¬ 
tween  his  son  and  daughter,  in  the  proportion  of  1  to 
f .  How  much  ought  each  to  receive  ? 

34.  In  a  mixture  of  tea  consisting  of  48  pounds, 
there  was  |  as  much  poor,  as  good  tea  :  how  much  of 
each  kind  was  there? 

35.  A  man  bought  a  cow  and  a  horse  for  $96  ;  the 
cow  cost  |  as  much  as  the  horse  ;  how  much  was  the 
cost  of  each  ? 

36.  Moses  has  only  -f  as  many  chestnuts  as  Aaron  ; 
and  both  have  40  quarts ;  how  many  belongs  to 
each  ? 

37.  Divide  the  number  49,  into  two  parts,  that  shall 
be  to  each  other  as  1  to  f. 

38.  A  hound  ran  60  rods  before  he  caught  a  fox; 
and  |  the  distance  the  fox  ran  before  he  was  caught, 
equaled  the  distance  he  was  ahead  when  they  started. 
How  far  did  the  fox  run,  and  how  far  in  advance  of 
the  hound  was  he,  when  the  chase  commenced  ? 

39.  The  sum  of  two  numbers  is  140,  and  the  larger 
is  to  the  smaller  as  1  to  £  ;  what  are  the  two  num¬ 
bers  ? 

40.  A  and  B  together  owe  $69,  but  B  owes  only  li¬ 
as  much  as  A  ;  how  much  does  each  owe? 

41.  Thomas  and  Thornton  found  $240,  but  could 
not  agree  about  the  division  of  it;  they,  therefore, 
threw  it  on  the  floor  and  each  got  what  he  could  ;  it 
so  happened  that  Thomas  got  only  f  as  much  as 
Thornton.  How  much  did  each  get  ? 

42.  In  a  certain  school  consisting  of  48  pupils,  there 
are  If  times  as  many  boys  as  girls  ;  how  many  boys, 
and  how  many  girls  in  the  school  ? 

43.  A  gold  and  a  silver  watch  were  bought  for  $160; 
the  silver  watch  cost  only  |  as  much  as  the  gold  one ; 
how  much  was  the  cost  of  each  ? 

12* 


138 


ALGEBRAIC  QUESTIONS. 


44.  Divide  the  number  17  into  two  parts,  that  shall 

be  to  each  other  as  §  to  j.  . 

45  A  farmer  had  180  sheep  m  two  fields,  and  j  ot 

the  number  in  the  first  field  equaled  }  of  the  number 

in  the  second  ;  how  many  in  each  field  ■ 

46.  Divide  88  into  two  parts  that  shall  be  to  each 

other  as  |  to  f.  ,  ,  , 

47  Ji  of  the  distance  a  hare  ran  after  a  hound  started 

in  pursuit,  equaled  the  distance  she  was  before  the 

hound  when  they  started;  how  far  did  the  hare  run 

before  she  was  caught,  provided  the  hound  ran  80 

rods  to  overtake  her  ?  •  .  .  , 

48.  A  and  B  started  from  the  same  point,  and  ran 

in  the  same  direction  ;  B  ran  60  rods  ;  then  T\  of  t  le 
distance  A  had  run  equaled  the  distance  A  was  ahead 
of  B.  How  much  did  A  gain  on  B  m  running  60 

rods  ^  . 

49.  A  fishing-rod  the  length  of  which  is  24  feet,  is 

in  two  parts ;  §  of  the  longer  part  equals  the  length 
of  the  shorter.  How  long  is  each  part* 

50  A  hound  ran  90  rods  before  he  caught  a  deer ; 
the  deer  ran  44  times  as  far  as  it  was  ahead  of  the 
hound  when  they  started,  before  it  was  overtaken.  How 
far  ahead  of  the  hound  was  the  deer  when  the  chase 

commenced  ?  _  , 

51  of  A’s  number  of  sheep  +  f  of  Bs  number, 

equals  900  ;  how  many  sheep  has  each,  provided  f  of 
B’s  number  is  twice  §  of  As  number  ? 


LESSON  XIII. 

1.  A  person  had  two  silver  cups,  and  only  one  cover 
for  both.  The  first  cup  weighed  6  oz.  It  the  first 
cup  be  covered,  it  will  weigh  twice  as  much  as  the 
second,  but  if  the  second  cup  be  covered  it  will  weigh 


ALGEBRAIC  QUESTIONS.  139 

3  times  as  much  as  the  first.  What  is  the  weight  of 
the  second  cup  and  cover? 

Solution. — By  the  last  condition  of  the  question,  3  times  6  oz., 
the  weight  of  the  first  cup,  or  18  ounces,  equals  the  weight  of 
the  second  cup  and  cover.  Consequently  the  two  cups  and 
cover  weigh  18+6  ounces,  which  are  24  ounces.  And  by  the 
first  condition,  the  first  cup  and  cover  weigh  twice  as  much  as 
the  second  cup.  Therefore  the  24  ounces  must  be  divided  into 
two  parts,  which  are  to  each  other  as  2  to  1.  One  of  these  parts 
will  be  the  weight  of  the  second  cup,  and  2  the  weight  of  the 
first  cup  and  cover,  &c. 

2.  A  lady  lias  two  silver  cups,  and  only  one  cover 
for  both.  The  first  cup  weighs  8  ounces.  The  first 
cup  and  cover  weigh  3  times  as  much  as  the  second 
cup ;  and  the  second  cup  and  cover  4  times  as  much 
as  the  first  cup.  What  is  the  weight  of  the  second 
cup  and  cover  ? 

3.  A  man  bought  a  hat,  a  coat,  and  a  vest  for  $40. 
The  hat  cost  $6 ;  the  hat  and  coat  cost  9  times  as 
much  as  the  vest.  What  was  the  cost  of  each  ? 

4.  A  boy  bought  a  squirrel,  a  rabbit,  and  a  bird. 
The  squirrel  cost  1 5  cents.  The  squirrel  and  rabbit 
cost  twice  as  much  as  the  bird  ;  and  the  rabbit  and 
bird  cost  3  times  as  much  as  the  squirrel.  What  was 
the  cost  of  the  bird  and  rabbit  respectively  ? 

5.  A  farmer  bought  a  cow,  an  ox,  and  a  horse ; 
the  cow  cost  $20.  The  cow  and  ox  together  cost  3 
times  as  much  as  the  horse ;  the  ox  and  horse 
together  cost  4  times  as  much  as  the  gow.  What  was 
the  cost  of  the  ox  and  horse  respectively  ? 

6.  A  man  bought  two  horses  and  a  saddle.  The 
younger  horse  cost  $40.  The  saddle  cost  j  as  much 
as  both  horses ;  and  the  younger  horse  cost  as  much 
as  the  other  horse  and  saddle  together.  What  did  the 
saddle  and  older  horse  cost  respectively  ? 

7.  A  man  traveled  three  successive  days.  The 
first  day  he  traveled  30  miles,  which  was  {  of  the  dis¬ 
tance  he  traveled  the  other  two  days  ;  and  4  times  the 


140 


ALGEBRAIC  QUESTIONS. 


distance  lie  traveled  the  second  day  equaled  the  dis¬ 
tance  lie  traveled  tlie  first  and  third  days.  How  fai 

did  he  travel  each  day  ?  * 

8.  A  is  worth  $1000,  and  B  and  C  together  are 
worth  9  times  as  much  as  A  ;  and  C  is  worth  |  as 
much  as  A  and  B.  How  much  is  B  and  C  worth 
respectively  ? 

9.  A’s  coat  cost  $20,  and  his  vest  and  hat  together 
cost  5  times  as  much  as  his  coat  ;  and  3  times  the  cost 
of  his  vest  equaled  the  cost  of  both  coat  and  hat. 
What  was  the  cost  of  his  vest  and  hat  respectively  ? 

10.  B’s  harness  cost  $120,  which  was  ^  of  the  cost 
of  his  horse  and  sleigh  ;  and  the  harness  and  horse 
together  cost  twice  as  much  as  the  sleigh.  How  much 
did  the  horse  and  sleigh  cost  respectively  ? 

11.  A  tree  in  falling  broke  into  three  unequal 
pieces.  The  top  piece  was  8  feet  long,  which  was 
of  the  length  of  the  other  two  pieces ;  and  3  times  the 
length  of  the  bottom  piece,  equals  the  length  ot  the 
other  two  pieces.  How  long  was  the  tree,  and  how 
long  was  each  piece? 

12.  Find  the  ages  of  A,  B,  and  C,  by  knowing  that 
A  is  20  years  old,  and  that  the  sum  of  B  and  C  s  age 
is  4  times  A’s  age  ;  and  that  C’s  age  is  4  of  the  sum 
of  A  and  B’s  age. 

13.  Find  the  fortunes  of  A,  B,  C,  I>,  E,  and  F,  by 
knowing  that  A  is  worth  $20,  which  is  \  as  much  as 
B  and  0  are  worth,  and  that  C  is  worth  1  as  much  as 
A  and  B  ;  and,  also  that  if  19  times  the  sum  of  A,  B, 
and  C’s  fortune  were  divided  in  the  proportion  of  f ,  4, 
and  \  it  would  respectively  give  f  of  D’s,  \  of  E’s  and 
|  of  F’s  fortune. 

14.  A  and  B  dug  a  100  rods  of  ditch  for  $100.  A 

received  10  shillings  a  rod  and  B  6  shillings  a  rod. 
Flow  many  rods  did  each  dig,  provided  each  received 
$50?  Ans.  A  dug  62|-  rods,  and  B  37£. 

Note.-— Consider  the  above  a  Penn,  or  N.  J.  question. 


REDUCTION. 


141 


CHAPTER  VIII. 
LESSON  I. 


Remark.— In  our  calculations  on  interest,  we  shall  reckon 
30  days  to  the  month,  and  12  months  to  the  year.  Althouo-h 
tli is,  mathematically  speaking,  will  not  produce  a  result  strictly 

accurate;  yet  it  will  be^  sufficiently  correct ,  for  all  practical  pur- 
poses. 

1.  Reduce  2  years  and  4  months  to  the  fraction  of 
a  year. 


Solution. — 4  months  is  what  part  of  a  year?  There  are  12 
months  in  1  year,  therefore  1  month  is  -D  0f  a  year.  and  4 
months  are  4  times  jL,  which  are  T%  or  $  of  a  year.  In  24  years 
how  many  thirds  ?  In  one  there  are  f,  therefore  3  times  the 
number  of  whole  ones  equal  the  number  of  thirds.  3  times  2 
are  6,  and  added  are  years. 

JST  Remark.— Always  reduce  a  fraction  to  its  lowest  terms 
before  perform  ing  any  other  operation  with  it. 

Pupils  may  not  be  able,  readily  to  discover  the  greatest  num¬ 
ber  that  will  divide  both  numerator  and  denominator ,  without  a 
remainder.  Consequently,  the  most  expeditious  way  will  be,  to 
continue  to  divide  by  the  least  number  that  is  contained  in  both 
numerator  and  denominator  without  a  remainder,  until  the 
fraction  is  reduced  to  its  lowest  terms. 


2.  Reduce  1  year  and  3  months  to  the  fraction  of  a 
year. 

3.  Reduce  3  years  and  5  months  to  the  fraction  of 
a  year. 

4.  Reduce  4  years  and  10  months  to  the  fraction  of 
a  year. 

5.  Reduce  7  years  and  9  months  to  the  fraction  of 
a  year. 

G.  Reduce  8  years  and  8  months  to  the  fraction  of 
a  year. 

7.  Reduce  12  years  and  7  months  to  the  fraction 
of  a  year. 

8.  Reduce  1 1  years  and  1 1  months  to  the  fraction 
of  a  year. 


-V**? 

r 


142 


KEDUCTI ON. 


9.  Reduce  6  years  and  6  months  to  the  fraction  of 
a  year. 

10.  Reduce  9  years  and  8  months  to  the  fraction  of 
a  year. 

11.  Reduce  2  years  4  months  and  15  days  to  the 
fraction  of  a  year. 

Solution. — 15  days  is  what  part  of  a  month?  There  are  30 
days  in  one  month,  therefore  1  day  is  of  a  month,  and  15 
days  are  15  times  ^  which  are  or  £  of  a  month.  4^  months, 
or  |  months,  is  what  part  of  a  year?  There  are  12  months  in 
1  year,  therefore,  1  month  is  of  a  year,  and  \  of  a  month,  is 
\  of  which  is  of  a  year ;  and  if  J  of  a  month  is  of  a 
year,  9  halves  are  9  times  which  are  or  §  of  a  year.  2£ 
years,  equal  Js-  years. 

12.  Reduce  4  years  7  months  and  6  days  to  the 
fraction  of  a  year. 

13.  Reduce  5  years  9  months  and  18  days  to  the 
fraction  of  a  year. 

14.  Reduce  1  year  7  months  and  18  days  to  the 
fraction  of  a  year. 

15.  Reduce  2  years  7  months  and  C  days  to  the 
fraction  of  a  year. 

Remark. — Omitting  the  intermediate  steps  in  the  analysis  we 
have : 

Solution. — 6  days  is  or  \  pf  a  month.  1 4  months  equal 
iyi  months.  -3/  months  equal  f  of  a  year.  2|  years  equal  ->53- 
years. 

16.  Reduce  3  years  o  months  and  6  days  to  the 
fraction  of  a  year. 

17.  Reduce  5  years  4  months  and  24  days  to  the 
fraction  of  a  year. 

18.  Reduce  6  years  5  months  and  18  days  to  the 
fraction  of  a  year. 

19.  Reduce  7  years  11  months  and  6  days  to  the 
fraction  of  a  year. 

20.  Reduce  10  years  10  months  and  12  days  to 
the  fraction  of  a  year. 


PERCENTAGE  AND  INTEREST.  143 


LESSON  Ii. 


Remark.—  Interest  is  money  due  for  the  use  of  money  bor¬ 
rowed  ;  and  is  estimated,  at  a  certain  rate  per  cent,  per  annum 
which  is  regulated  by  law.  ’ 

The  sum  on  which  the  interest  is  paid  is  called  the  Principal. 
ine  sum  ot  the  principal  and  interest  is  called  the  Amount 

By  6  per  cent,  is  meant,  6  cents  on  100  cents,  $6  on  $100,  or 
b  on  100  whatever  be  the  denomination.  Hence,  at  6  per  cent, 
ion  or  3(r  the  principal  equals  the  interest. 

When  no  time  is  specified  1  year  is  understood. 

1..  At  4  per  cent.,  what  part  of  the  principal  equals 
the  interest.  1 


.  Solution.— If  the  interest  of  100  cents  is  4  cents,  of  1  cent  it 
is  yfo  of  4  cents  which  is  T~  or  J,  of  a  cent.  Therefore,  at  4 
per  cent.,  -Jj  of  the  principal  equals  the  interest. 

2.  At  2  per  cent.,  what  part  of  the  principal  equals 

the  interest  ?  1 

3.  At  5  pci  cent.,  what  part  of  the  principal  equals 

the  interest  ?  11 

4.  At  G  pci  cent.,  what  part  of  the  principal  equals 

the  interest  ?  1 

5.  At  8  per  cent.,  what  part  of  the  principal  equals 

the  interest  ?  r  ^ 

G.  At  10  per  cent.,  what  part  of  the  cost  equals  the 
gain  ? 

t .  At  7  pei  cent.,  what  part  of  the  principal  equals 
the  interest  ?  1 

8.  At  12  per  cent.,  wrhat  part  of  the  cost  equals  the 
gam  ? 

9..  At  lb  per  cent.,  what  part  of  the  principal  equals 
the  interest  ?  * 

10.  What  is  the  interest  of  $80  for  1  year,  at  15 
per  cent.  ? 


SoLunoN.-At  15  per  cent.  T^,  or  ^  of  the  principal  equals 
the  interest.  £s  of  $80  is  $12,  the  interest. 


11.  W hat  is  the  interest  of  $120  for  1  year,  at  25 
per  cent.  ?  J 


144 


PER  CE  NT. 


12.  What  is  the  interest  of  $510  for  1  year,  at  20 

per  cent.  ? 

13.  What  is  the  interest  of  $750  for  1  year,  at  24 
per  cent.  ? 

14.  A  man  paid  $120  for  a  wagon  and  sold  it,  at  a 
gain  of  30  per  cent. ;  how  much  was  his  gain  ? 

Solution.— If  he  gained  30  per  cent,  he  gained  yhb,  or  T3ff  of 
the  cost.  t3o  of  $120  is  $36,  the  gain. 

15.  A  tailor  sold  a  coat  that  cost  him  $25,  at  a  gain 
of  32  per  cent. ;  how  much  did  he  gain  ? 

16.  A  man  sold  a  quantity  of  goods  that  cost  him 
$840*  at  a  gain  of  75  per  cent. ;  how  much  did  he 
gain  ? 

17.  Edward  spent  85  per  cent,  of  $120  for  a  suit  of 
clothes.  How  much  did  his  clothes  cost  him? 

18.  Henry’s  watch  cost  $180,  he  sold  it  at  a  loss  of 
15  per  cent. ;  how  much  did  he  receive  for  it? 

19.  A  boy  sold  a  quantity  of  candies  that  cost  him 
50  cents,  at  a  gain  of  120  per  cent.  ;  how  much  did 
he  receive  for  them  ? 

20.  Jacob  sold  a  horse  that  cost  him  $240,  at  a  loss  of 
25  per  cent. ;  how  much  did  he  receive  for  the  horse  ? 

- — ♦  - 

LESSON  III. 

Remark. — "When  we  say  of  the  principal  equals  the  in¬ 
terest,  it  will  be  understood,  that,  a  twentieth  part  of  the  princi¬ 
pal,  whatever  be  the  denomination ,  will  equal  the  interest. 

4  1.  If  _3_  0f  the  principal  equals  the  interest,  what  is 

the  rate  per  cent.  ? 

Solution. — If  the  interest  of  1  cent  is  of  a  cent,  the  in¬ 
terest  of  100  cents  is  100  times  or  ,  or  6  cents.  There¬ 
fore,  it  is  6  per  cent. 

2.  If  J_  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent.  ? 

3.  If  _2_  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent.? 


PER  CENT. 


145 


4=  If  °f  the  c°st  equals  the  gain,  what  is  the 
rate  per  cent.  ? 

5*  If  o35  ot  the  cost  equals  the  gain,  what  is  the 
rate  per  cent.  ? 

6-  If  2V  °f  the  principal  equals  the  interest,  what  is 
the  rate  per  cent.  ? 

7.  If  Ty  of  the  cost  equals  the  gain,  what  is  the 
rate  per  cent.? 

8.  If  the  interest  of  $44  for  1  year  is  $4,  what  is 
the  rate  per  cent.  ? 

Solution. — If  the  interest  of  $44  is  $4,  ¥4T,  or  -J  of  the 
principal  equals  the  interest.  If  the  interest  of  $1  is^-L  the 
interest  on  $100  is  100  times  $yLi-,  or  -TP-0-,  or  $9—.  Therefore, 
$44  in  1  year  will  give  $4  interest,  at  9Ty  per  cent. 

9.  If  the  interest  of  $72  for  1  year  is  $6,  what  is 
the  rate  per  cent.  ? 

10.  If  the  interest  of  $96  for  1  year  is  $12,  what  is 
the  rate  per  cent.  ? 

11.  B  bought  a  horse  for  $100  and  sold  it  for  $109, 
how  much  did  he  gain  per  cent.  ? 

12.  A  woman  bought  a  quantity  of  oranges  for  75 
cents  and  sold  them  for  84  cents  5  how  much  did  she 
gain  per  cent.  ? 

13.  A  merchant  bought  a  quantity  of  books  for  $200, 
and  sold  them  for  $228 ;  how  much  did  he  rrain  per 
cent.  ? 

14.  Thornton  bought  a  boat  for  $50  and  sold  it  for 
$80  ;  what  was  his  gain  per  cent.  ? 

15.  Harvey  bought  a  hogshead  of  molasses  for  $25 
and  sold  it  for  $314  •  bow  much  did  he  gain  per  cent.  ? 

16.  Bought  a  knife  for  37  cents  and  sold  it  for  574 
cents  ;  what  was  the  gain  per  cent.  ? 

17.  A  stationer  sold  a  quantity  of  paper  for  f  of 
what  it  cost  him ;  how  much  did  he  gain  per  cent.4? 

_  18*  James  received  for  his  horse  f  of  what  it  cost 
him  ;  how  much  did  he  gain  per  cent.  ? 

13 


146 


PEE  CENT. 


19.  A  man  sold  a  barrel  of  pork  for  of  what  it 
cost  him  ;  how  much  did  he  gain  per  cent.  ? 

20.  The  interest  of  $500  for  4  years  is  $240  ;  what 
is  the  rate  per  cent.  ? 

Solution. — If  the  interest  of  $500  for  4  years  is  $240,  for  1 
year  it  is  }  of  $240,  or  $60.  Therefore,  or  YS  of  the  Prin' 
cipal  equals  the  interest.  If  the  interest  of  $1  for  1  year  is 
$#5,  the  interest  of  $100  is  100  times  or  or  $12* 
Therefore,  it  is  12  per  cent. 

21.  A  man,  being  asked,  at  what  per  cent,  his  money 
was  on  interest,  replied,  I  receive  $120  interest  in  10 
years  for  $240  ;  what  was  his  rate  per  cent.  ? 

22.  A  bought  a  horse  for  $150  and  sold  it  for  $180; 
what  was  liis  gain  per  cent.? 

23.  Elisha  bought  10  horses  for  $800,  and  sold  8 
of  them  for  what  they  all  cost ;  what  was  his  gain  per 
cent.  ? 

24.  Jg-  of  the  money  C  paid  for  books,  is  £  of  what 
he  gained  by  selling  them.  How  much  did  he  gain 
per  cent.  ? 

25.  ¥ j  of  the  money  I  have  on  interest,  is  4  times 
the  yearly  interest  received.  What  is  the  rate  per 
cent.  ? 

26.  if  of  the  cost  of  A’s  merchandise,  is  f  of  what 
he  gained  when  he  sold  it.  What  was  his  gain  per 
cent.  ? 

27.  of  the  cost  of  B’s  wagon,  is  f  of  what  ho 
gained  by  selling  it.  What  did  he  gain  per  cent,  ? 

28.  A  book  was  sold  for  f  of  f  of  what  it  cost. 
What  was  the  loss  per  cent.  ? 

29.  |  of  |  of  the  cost  of  a  sleigh,  was  what  it  was 
sold  for.  What  was  the  gain  per  cent.  ? 

30.  A  merchant  bought  a  quantity  of  goods  for 
$860  and  sold  them  for  $1075  ;  how  much  did  he  gain 
per  cent.  ? 


V 


PERCENTAGE, 


147 


*  > 


LESSON  IV. 

!•  At  5  per  cent,  for  4  years,  what  part  of  the  prin¬ 
cipal  equals  the  interest  ? 

Solution.— If  the  interest  of  $1  for  1  year  is  5  cents,  for  4 
years  it  is  4  times  5  cents,  or  20  cents.  Therefore,  T^°0,  or  £  of 
the  principal  equals  the  interest. 

2.  At  6  per  cent,  for  5  years,  what  part  of  the  prin¬ 
cipal  equals  the  interest? 

3.  At  3  per  cent,  for  2  years,  what  part  of  the  prin¬ 
cipal  equals  the  interest  ? 

4.  At  4  per  cent,  for  3  years,  what  part  of  the  prin¬ 
cipal  equals  the  interest  ? 

5.  At  6  per  cent,  for  3  years,  what  part  of  the  prin¬ 
cipal  equals  the  interest  ? 

6.  At  4  per  cent,  for  3  years,  what  part  of  the  prin¬ 
cipal  equals  the  interest  ? 

7.  At  9  per  cent,  for  6  years,  what  part  of  the  prin¬ 
cipal  equals  the  interest  ? 

8.  At  8  per  cent,  for  5  years,  what  part  of  the  prin¬ 
cipal  equals  the  interest  ? 

9.  At  4  per  cent,  for  6  years,  what  part  of  the  prin¬ 
cipal  equals  the  interest  ? 

10.  At  6  per  cent,  for  8  years,  what  part  of  the 
principal  equals  the  interest  ? 

11.  At  10  per  cent  for  5  years,  what  part  of  the 
principal  equals  the  interest  ? 

12.  At  G  per  cent,  for  4  years  and  8  months,  what 
part  of  the  principal  equals  the  interest  ? 

Remark. — It  is  expected  that  pupils  thoroughly  understand 
every  lesson  they  have  been  over ;  and  are,  therefore,  prepared 
to  arrive  at  results,  understandingly,  without  giving  the  entire 
analysis  of  all  parts  of  the  question. 

Solution. — 8  months  is  or  §  of  a  year.  4§  years  equal 
Ja4-  years.  If  the  interest  of  $l  for  1  year  is  6  cents,  for 
years  it  is  ’A  times  6  cents,  or  28  cents.  Therefore,  or 
23  of  the  principal  equals  the  interest. 


148 


INTEREST. 


13.  At  4  per  cent,  for  6  years  and  6  months,  what 
part  of  the  principal  equals  the  interest? 

14.  At  6  per  cent,  for  5  years  and  4  months,  what 
part  of  the  principal  equals  the  interest? 

15.  At  10A  per  cent,  for  1  year  and  G  months,  what 
part  of  the  principal  equals  the  interest? 

16.  At  4|  per  cent,  for  9  years,  what  part  of  the 
principal  equals  the  interest  ? 

17.  At  3f  per  cent,  for  2  years  and  2  months,  what 
part  of  the  principal  equals  the  interest  ? 

18.  At  6|  per  cent,  for  4  months  and  24  days,  what 
part  of  the  principal  equals  the  interest  $ 

19.  At  7  a  per  cent,  for  10  months,  what  part  of  the 
principal  equals  the  interest  ? 

20.  At  3T\  per  cent,  for  2  years,  4  months  and  15 
days,  what  part  of  the  principal  equals  the  interest  ? 


LESSON  V. 

1.  What  is  the  interest  of  $50  for  4  years,  at  G  per 
cent.  ? 

Solution. — If  the  interest  of  $1  for  1  year  is  6  cents,  for  4 
years  it  is  4  times  6  cents,  or  24  cents.  Therefore,  T~A,  or  -A 
of  the  principal  equals  the  interest.  A  of  $50  is  $12,' the  in¬ 
terest. 

2..  What  is  the  interest  of  $10  for  2  years,  at  5  per 
cent.  ? 

3.  What  is  the  interest  of  $48  for  G  years,  at  5  per 
cent.  ? 

4.  What  is  the  interest  of  #70  for  7  years,  at  5  per 
lent.  ? 

5.  What  is  the  interest  of  $G8  for  5  years,  at  6  per 
cent.  ? 

G.  W  hat  is  the  interest  ol  $70  for  2  years,  at  5  per 
cent.  ? 

A  What  is  the  interest  of  $75  for  o  years,  at  3  per 
cent.  ? 


INTEREST. 


149 


$ 


8.  What  is  the  interest  of  $120  for  8  years,  at  5 
per  cent.  ? 

9.  What  is  the  interest  of  $100  for  10  years,  at  6 
per  cent.  ? 

10.  What  is  the  interest  of  $140  for  12  years,  at  5 
per  cent.  ? 

11.  What  is  the  interest  of  $150  for  5  years,  at  3 
per  cent.  ? 

12.  AVhat  is  the  interest  of  $145  for  6  years,  at  5 
per  cent.  ? 

13.  What  is  the  interest  of  $200  for  10  years,  8 
per  cent.  ? 

14.  What  is  the  interest  of  $250  for  3  years,  at  8 
per  cent.  ? 

15.  AVhat  is  the  interest  of  $220  for  11  years,  at  10 
per  cent.  ?  • 

16.  AVhat  is  the  interest  of  $500  for  9  years,  at  8 
per  cent.  ? 

17.  What  is  the  interest  of  $250  for  12  years,  at  6 
per  cent.  ? 

18.  AVhat  is  the  interest  of  $500  for  8  years,  at  12 
per  cent.  ? 

19.  What  is  the  interest  of  $200  for  9  years,  at  3 
per  cent.  ? 

20.  AVhat  is  the  interest  of  $405  for  10  years,  at  8 
per  cent.  ? 

21.  AVhat  is  the  interest  of  $50  for  2  years  and  2 
months,  at  6  per  cent.  ? 

Solution. — 2  months  is  of  a  year.  21  years  equals 
years.  If  the  interest  of  $1  for  1  year  is  6  cents,  for  yt  years 
it  is  times  6  cents,  or  13  cents.  Therefore,  Tyh  of  the  prin¬ 
cipal  equals  the  interest.  ^  0f  $50  is  or  $6.50,  the  in¬ 
terest. 

22.  AVhat  is  the  interest  of  $25  for  4  years  and  3 
months,  at  4  per  cent.  ? 

23.  What  is  the  interest  of  $80  for  5  years  and  5 
months,  at  G  per  cent.  ? 


13* 


150 


INTEREST. 


24.  What  is  the  interest  of  $60  for  8  years  and  6 
months,  at  6  per  cent.  ? 

25.  What  is  the  interest  of  $240  for  3  years  and  9 
months,  at  6  per  cent.  ? 

26.  What  is  the  interest  of  $75  for  4  years  and  8 
months,  at  9  per  cent.  ? 

27.  What  is  the  interest  of  $50  for  2  years  and  9 
months,  at  6  per  cent.  ? 

28.  What  is  the  interest  of  $80  for  12  years  and  10 
months,  at  6  per  cent.  ? 

29.  What  is  the  interest  of  $69  for  8  years  and  4 
months,  at  2  per  cent.  ? 

30.  What  is  the  interest  of  $60  for  4  years  and  8 
months,  at  3  per  cent.  ? 

31.  What  is  the  interest  of  $600  for  2  years  4 
months  and  1 5  days,  at  4  per  cent.  ? 

Solution'. — 15  days  is  J  of  a  month.  4J  months  equals  9 
months.  months  equals  or  |  of  a  year.  years  equal 
y1-  years.  If  the  interest  of  $1  for  1  year  is  4  cents,  for  -y9- 
years  it  is  -\9-  times  4  cents,  or  -V-  cents.  Therefore,  of  the 

principal  equals  the  interest.  -J/o  $600  is  $57,  the  interest. 

32.  What  is  the  interest  of  $300  for  5  years  9 
months  and  1 8  days,  at  5  per  cent.  ? 

33.  What  is  the  interest  of  $550  for  4  years  7 
months  and  6  days,  at  10  per  cent.? 

34.  What  is  the  interest  of  $500  for  1  year  7 
months  and  18  days,  at  6  per  cent,? 

35.  What  is  the  interest  of  $250  for  3  years  7 
months  and  6  days,  at  4  per  cent.  ? 

36.  What  is  the  interest  of  $250  for  3  years  3 
months  and  6  days,  at  6  per  cent.  ? 

37.  What  is  the  interest  of  $50  for  6  years  4  months 
and  24  days,  at  5  per  cent.? 

38.  What  is  the  interest  of  $75  for  2  years  11 
months  and  6  days,  at  1 5  per  cent.  ? 

39.  What  is  the  interest  of  $150  for  2  years  6 
months  and  1 2  days,  at  1 5  per  cent.  ? 


INTEREST. 


151 


40.  What  is  the  interest  of  $300  for  2  years  9 
months  and  18  days,  at  If  per  cent.? 

- -»♦«  ■»>.»■ - 

LESSON  VI. 

1.  What  is  the  amount  of  $75  for  2  years,  at  6  per 
cent  ? 

Solution. — If  the  interest  of  $1  for  1  year  is  6  cents,  for  2 
years  it  is  2  times  6  cents,  or  12  cents.  Therefore,  -J/¥,  or  qt  of 
the  principal  equals  the  interest,  of  $15  is  $9,  the  interest; 
to  which  add  $75,  the  principal,  and  we  have  $84,  the  amount. 

2.  What  is  the  amount  of  $90  for  3  years,  at  7  per 
cent.  ? 

3.  What  is  the  amount  of  $100  for  4  years,  at  5  per 
cent.  ? 

4.  What  is  the  amount  of  $160  for  10  years,  at  5 
per  cent.  ? 

5.  What  is  the  amount  of  $160  for  8  years,  at  5  per 
cent.  ? 

6.  What  is  the  amount  of  $200  for  12  years,  at  5 
per  cent.  ? 

7.  What  is  the  amount  of  $210  for  2  years  and  6 
months,  at  4  per  cent.? 

8.  What  is  the  amount  of  $250  for  4  years  and  3 
months,  at  8  per  cent.  ? 

9.  What  is  the  amount  of  $240  for  4  years  and  3 
months,  at  3  per  cent.  ? 

10.  What  is  the  amount  of  $500  for  3  years  3 
months  and  6  days,  at  6  per  cent.? 

11.  What  is  the  amount  of  $200  for  5  years  4 
months  and  24  days,  at  5  per  cent,  ? 

• - »>« •»  »«»■ - 

LESSON  VII. 

1.  What  principal  will  in  4  years,  at  6  per  cent., 
give  $12  interest? 

Solution. — If  the  interest  of  $1  for  1  year  is  6  cents,  for  4 


152 


INTEREST. 


years  it  is  4  times  6-  cents,  or  24  cents.  Therefore,  y (4q,  or  ~ ^  of 
the  principal  equals  the  interest,  which  is  $12.  If  ^  of  the 
principal  is  $12,  of  the  principal  is  £  of  $12,  or  $2 ;  and  If 
or  the  principal,  is  25  times  $2,  or  $50. 

2.  What  principal  will  in  6  years,  at  4  per  cent., 
give  $36  interest  ? 

3.  What  principal  will  in  4  years,  at  5  per  cent., 
give  $30  interest  ? 

4.  What  principal  will  in  8  years,  at  7  per  cent., 
give  $42  interest? 

5.  What  principal  will  in  10  years,  at  7  per  cent., 
give  $140  interest? 

6.  What  principal  will  in  4  years  and  6  months,  at 
6  per  cent.,  give  $54  interest  ? 

7.  What  principal  will  in  4  years  and  3  months,  at 

5  per  cent.,  give  $102  interest? 

8.  What  principal  will  in  4  years,  and  3  months,  at 
8  per  cent.,  give  $51  interest  ? 

9.  How  much  money  has  that  man  on  interest,  who, 
at  the  expiration  of  4  years  and  4  months,  at  6  per 
cent.,  receives  $260  interest? 

10.  At  the  expiration  of  2  years  and  4  months,  at 

6  per  cent.,  a  man  received  $49  interest.  How  much 
money  had  he  on  interest  ? 

11.  A  is  worth  twice  as  much  as  B,  and  the  in¬ 
terest  of  their  united  fortunes  for  4  years  and  2 
months,  at  6  per  cent.,  is  $600.  How  much  is  each 
worth  ? 

12.  The  interest  on  the  cost  of  B’s  store  and  house, 
for  1  year  and  6  months,  at  4  per  cent.,  would  he  $270. 
What  was  the  cost  of  each,  provided  the  store  cost  y 
as  much  as  the  house? 

13.  If  the  money  B  paid  for  a  sheep,  a  cow,  and 
horse,  was  put  on  interest  for  4  years  and  6  months, 
at  4  "per  cent.,  it  would  give  $18  interest.  What  was 
the  cost  of  all,  and  of  each  respectively,  provided  the 
sheep  cost  y  as  much  as  the  cow,  and  the  cow,  4  as 
much  as  the  horse  ? 


INTEREST. 


153 


LESSON  VIII. 

1.  What  principal  will  in  4  years,  at  5  per  cent., 
amount  to  $360  ? 

Solution. — If  the  interest  of  $1  for  1  year  is  5  cents,  for  4 
years  it  is  4  times  5  cents,  or  20  cents.  Therefore,  T2^°ff,  or  4  of 
the  principal  equals  the  interest ;  to  which  add  |,  the  principal, 
and  we  have  |  of  the  principal  equal  to  the  amount,  $360.  If 
4  of  the  principal  is  $360,  4  of  the  principal  is  4  of  $360,  which 
is  $60,  and  j  (the  principal),  is  5  times  $60,  which  are  $300. 

2.  What  principal  will  in  3  years,  at  6  per  cent., 
amount  to  $118  ? 

3.  What  principal  will  in  6  years,  at  10  per  cent., 
amount  to  $120  ? 

4.  What  principal  will  in  10  years,  at  7  per  cent., 
amount  to  $1 V0? 

5.  What  principal  will  in  4  years,  at  5  per  cent., 
amount  to  $660  ? 

6.  A  is  worth  4  as  much  as  B ;  and  the  interest  on 
their  united  fortunes  for  2  years,  at  5  per  cent.,  is  $880. 
What  is  each  of  their  fortunes?  . 

V.  A  merchant  sold  a  quantity  of  cloth  for  $214, 
and  thereby  gained  V  per  cent.  What  did  the  cloth 
cost  him  ? 

8.  What  principal  will  in  2  years,  at  V  per  cent., 
amount  to  $1140  ? 

9.  What  principal  will  in  10  years  and  8  months, 
at  9  per  cent.,  amount  to  $490  ? 

10.  The  amount  due  on  a  note,  which  had  been  on 
interest  6  years  and  2  months,  at  6  per  cent,  was 
$274.  What  was  the  face  of  the  note? 

11.  What  principal  will  in  12  years  and  9  months, 
at  4  per  cent.,  amount  to  $302  ? 

12.  If  4  of  A’s  fortune  for  4  years  and  6  months,  at 
6  per  cent.,  amounts  to  $127;  what  is  his  whole  for¬ 
tune  ? 

13.  If  |  of  B’s  fortune,  being  put  on  interest  for  3 


154 


INTEREST. 


years  3  months  and  6  days,  at  15  per  cent.,  amount  to 
$149  ;  what  is  his  whole  fortune  ? 

14.  Mary,  being  asked  how  much  money  she  had  on 
interest,  and  at  what  per  cent.,  replied;  the  principal 
and  rate  per  cent,  are  such  that  in  5  years  the  amount 
would  be  $750,  and  in  7  years,  $810.  What  was  the 

principal  and  the  rate  per  cent.  ? 

15.  A  man  sold  two  horses  for  $240,  losing  on  the 
first  20  per  cent.,  gaining  on  the  other  20  per  cent. ; 
what  was  the  value  of  each  horse,  provided  he  received 
for  the  second  3  times  as  much  as  for  the  first  ? 

16.  The  amount  of  Robert’s  capital  for  a  certain 
time,’ at  4  per  cent,  is  $360,  and  for  the  same  time,  at 
7  per  cent,  it  is  $405  ;  required  his  capital  and  the 

time. 


LESSON  IX. 

1.  In  what  time  will  $40,  at  6  per  cent.,  give  $12 
interest  ? 

Solution. — If  the  interest  of  $40  is  $12,  or  T3^  of  the 
principal  equals  the  interest.  If  the  interest  of  $1  for  1  year  is 
\  of  a  dollar,  of  $100,  it  is  1 00  times  $T3o,  or  $30.  If  it  require 
1  year  for  $100  to  give  $6  interest,  to  give  $30  interest  it  will 
require  as  many  years  as  $6  is  contained  times  in  $30,  or  5 
years. 

2.  In  what  time  will  $60,  at  5  per  cent.,  give  $18 
interest  ? 

3.  In  what  time  will  $90,  at  7  per  cent.,  give  $27 
interest  ? 

4.  In  what  time  will  $100,  at  6  per  cent.,  give  $10 
interest  ? 

5.  In  what  time  will  $120,  at  10  per  cent.,  give 
$120  interest? 

6.  In  what  time  will  $250,  at  6  per  cent.,  give  $20 
interest  ? 


PER  CENT. 


155 


V.  In  what  time  will  $40,  at  I  per  cent.,  give  $8.40 
interest  ? 

8.  In  what  time,  at  8  per  cent.,  will  $30  give  $9.60 
interest  ? 

9.  In  what  time,  at  6  per  cent.,  will  $10  give  $2.40 
interest  ? 

10.  In  what  time,  at  4  per  cent.,  will  $20  give 
$5.60  interest  ? 


- - - 

LESSON  X. 

1.  At  what  per  cent.,  will  $50,  in  1  year  and  6 
months,  or  (li  years),  give  $6  interest? 

Solution.— If  the  interest  of  $50  for  1J,  or  %  years  is  $6,  for 
i  °f  a  year  it  is  £  of  $6,  or  $2 ;  and  for  f,  or  1  year,  it  is  2  times 
$2,  or  $4.  Therefore,  or  ^  of  the  ,  principal  equals  the 
annual  interest.  If  the  interest  of$l  for  1  year  is  $  A ,  of  $100, 
it  is  100  times  $A>  or  $8.  Therefore,  it  is  8  percent. 

2r  At  what  per  cent.,  will  $40  annually  give  $2 
interest  ? 

3.  At  what  per  cent.,  will  $80  annually  give  $3.20 
interest  ? 

4.  At  what  per  cent.,  will  $120  annually  give  $12 
interest  ? 

5.  At  what  per  cent.,  will  $120  in  4  years,  give  $20 
interest  ? 

6.  At  what  per  cent.,  will  $100  in  3  years,  give  $30 
interest  ? 

V.  At  what  per  cent.,  will  $5  in  14  years,  give  $7 
interest  ? 

8.  At  what  per  cent.,  will  $25  in  1  year  and  9 
months,  give  $3.50  interest  ? 

9.  At  what  per  cent.,  will  $80  in  5  years  and  8 
months,  give  $34  interest? 

10.  At  what  per  cent.,  will  $500  in  7  years  and  6 
months,  give  $15  interest? 


156 


PER  CENT. 


11.  At  what  per  cent.,  will  $600  in  2  years  4  months 
and  15  days,  give  $57  interest? 


LESSON  XI. 

1.  At  what  per  cent.,  will  $10  in  4  years,  amount  to 

$12? 

Remark  —From  the  amount  subtract  the  principal,  and  the 
rematadm  Will  be  the  interest.  Them  proceed  as  m  the  pre- 
ceding  lesson. 

2.  At  what  per  cent.,  will  $12  in  3  years,  amount  to 

what  per  cent,  will  $20  in  6  years,  amount 

t0  412  At  what  per  cent.,  will  $24  in  10  years,  amount 

t0  5  3  At  what  per  cent.,  will  $30  in  7  years,  amount  to 

*36.3At  what  per  cent.,  will  $50  in  10  years,  amount  to 

S77.?At  what  per  cent.,  will  $36  in  5  years,  amount 

t0  If  At  what  per  cent,  will  a  given  principal  double 
itself,  in  20  years  ? 

Solution— A  given  principal  ^ 

100  per  cent. ;  and  in  20  years,  at  *  of  100  pel  cent.,  or 

per  cent.  .  .  .  ,  ,  , 

9.  At  what  per  cent,  will  a  given  principal  double 

^lO.'At  what  per  cent,  will  a  given  principal  double 
itself,  inji  yeiws^  ^  ^  ^  ^  principal  double 

'tS^L2.1  At  what  per  cent,  will  $80  in  7  years  give  $80 
interest  ? 


PER  CENT. 


157 


13.  At  what  per  cent.,  will  $640  in  6  years  give 
$640  interest  ? 

14.  At  what  per  cent.,  will  25  cents  in  8  years  give 
25  cents  interest? 

15.  At  what  per,  cent.,  will  $97  in  9  years  give  $97 
interest  ? 

16.  At  what  per  cent.,  will  $372  in  25  years  give 
$372  interest? 

1*7.  At  what  per  cent.,  will  $1  in  30  years  give  $1 
interest  ? 

18.  At  what  per  cent.,  will  $15  in  124-  years  give 
$15  interest? 

19.  At  what  per  cent.,  will  $42  in  144  years  give 
$42  interest  ? 

20.  At  what  per  cent.,  will  5  cents  in  16|-  years  give 
5  cents  interest  ? 


- - -»’«<»«■»■ - 

LESSON  XII. 

1.  In  what  time  will  a  given  principal  double  itself 
at  5  per  cent.  ? 

Solution. — A  given  principal  will  double  itself  in  100  years, 
at  1  per  cent.,  and,  at  5  per  cent.,  in  V  of  100  years,  which  is  20 
years. 

2.  In  wrhat  time  will  a  given  principal  double  itself, 
at  4  per  cent.  ? 

3.  In  what  time  will  $25,  at  3  per  cent.,  give  $25 

interest  ?  1  ’  b 

.  4*  In  wLat  time  will  $275,  at  6  per  cent.,  give  $275 
interest  ? 

5.  In  what  time  will  a  given  principal  double  itself, 
at  2  per  cent.  ? 

6.  In  what  time  will  $4,  at  7  per  cent.,  give  $4  in¬ 
terest  ?  1  ’  b 

.  w^at  time  will  $94,  at  9  per  cent.,  give  $94 

interest  ?  & 


14 


158 


pee  cent. 


8.  In  what  time  will  5  cents,  at  8  per  cent.,  give  5 

cents  interest  •  .  djo*? 

9.  In  what  time  will  $3§  at  10  per  cent.,  give  $3-^ 

interest ?  • 

10.  In  what  time  will  1  dime,  at  12 {  per  cent.,  gne 

1  dime  interest  ? 


LESSON  XIII.  * 

1.  Bought  a  bushel  of  grass-seed,  for  $5  and  sold  it 
for  $7  ;  what  was  the  gain  per  cent,  ? 

Solution.— Since  it  was  bought  for  $5  and  sold  for  $7,  the 
gain  must*  have  been  $7-$5  which  is  $2  Therefore  j  of  the 
lost  equals  the  gain.  If  on  $1  I  gam  $f,  on  $100  I  will  gam 
100  times  $f?  or  $40.  Therefore,  the  gam  is  40  per  cent. 

2.  A  hook  was  bought  for  $2,  and  sold  lor  $3  ;  what 

was  the  gain  per  cent.  ?  „  .  ^ 

3.  A  shawl  cost  $5,  and  was  sold  for  $8;  what  was 

the  gain  per  cent.  ?  .  -  *0fS . 

4»  A  cow  was  bought  for  $20,  and  sold  oi  $i.o  , 

what  was  the  gain  per  cent.  \ 

5  A  merchant  bought  a  hogshead  of  molasses  tor 

$80,  and  sold  it  for  $95 ;  what  did  he  gam  per ‘cent.  . 

6.  A  barrel  of  pork  cost  $12,  and  was  sold  ioi  $11 , 

what  was  the  loss  per  cent.  ?  . ,  *  . 

7.  A  horse  was  bought  for  $140,  and  sold  lor  $  , 

what  was  the  loss  per  cent. j. 

8.  Bought  an  orange  for  4  cents,  and  sold  it  lor  o 

cents  ;  what  was  the  gain  per  cent.  ?  .  » 

9.  Bought  a  melon  for  15  cents,  and  sold  it  lor 

cents ;  what  was  the  gain  per  cent.  ?  .  «  Q 

10.  Bought  a  hook  for  5  dimes,  and  sold  it  lor  8 

dimes:  what  was  the  gain  per  cent.? 

11.  Bought  a  quantity  of  silk  for  $120,  and  sold  it 

for  $200  ;  what  was  the  gain  per  cent.  ? 

12.  A  boy  sold  melons,  at  the  rate  of  10  cent* 


PERCENTAGE. 


159 


apiece,  A  of  which  equaled  his  gain ;  how  much  would 
he  have  gained  per  cent.,  if  he  had  sold  them,  at  12 
cents  apiece  ? 

13.  A  merchant  sold  sugar,  for  $80  a  hogshead, 
and  thereby  cleared  Tlw  of  his  money  ;  if  he  had  sold 
it,  at  $92  a  hogshead,  what  would  he  have  gained  per 
cent.  ? 

14.  A  quantity  of  cloth  was  bought  for  $36,  and 
sold  for  $43  ;  what  was  the  gain  per  cent.  ? 

15.  A  horse  was  bought  for  $100,  and  sold  for  $95  ; 
what  was  the  loss  per  cent.  ? 

16.  A  man  sold  a  horse  for  $120,  and  thereby 
cleared  a  of  its  cost ;  how  much  would  he  have  lost 
per  cent.,  if  he  had  sold  him  for  $80  ? 

17.  What  per  cent,  of  a  is  a  ?  Of  §  is  a  ?  Of  §  is 
A*  of  I  is  f?  Off  is  f?  Of  2i  is  f  ?  Of  3i  is  2tV? 

18.  |  of  $6  is  what  per  cent,  of  i  of  $100  ? 

19.  -f  of  $28  is  |  of  what  per  cent,  of  f  of  $300  ? 

20.  Walter  sold  a  horse  for  $120,  and  thereby 
cleared  i  of  its  cost ;  what  would  he  have  lost  per 
cent,  by  selling  it  for  $80  ? 

- 4M4-  »♦» - 

LESSON  XIV. 

1.  A  man  bought  a  cow  for  $20  ;  for  what  must  he 
sell  her,  to  gain  5  per  cent,  on  the  cost  ? 

Solution. — If  he  gains  5  per  cent,  he  gains  or  ^  of  the 
cost.  of  $20  is  $1»  the  gain.  Therefore,  to  gain  5  per  cent, 
he  must  sell  the  cow  for  $20  +  $1,  or  $21. 

2.  A  man  bought  a  yoke  of  oxen  for  $100;  how 
must  he  sell  them,  to  gain  6  per  cent,  on  the  cost  ? 

3.  A  man  bought  a  barrel  of  rum  for  $10  ;  for  what, 
must  be  sell  it,  to  gain  10  per  cent,  on  the  cost? 

4.  A  gallon  of  wine  was  bought  for  20  dimes ;  how 
must  it  be  sold  a  pint,  to  gain  20  per  cent,  on  the 
cost? 


160 


DISCOUNT. 


5.  A  hogshead  of  molasses  cost  $20 ;  for  what 
ought  it  to  be  sold  a  gallon,  to  gain  40  per  cent,  on  the 
cost  ? 

6.  B  bought  a  horse  for  $80,  and  by  selling  it,  lost 
5  per  cent,  on  the  cost ;  for  what  did  he  sell  it  ?  • 

V.  A  wagon  cost  $140,  and  was  sold  for  5  per  cent, 
less  than  it  cost ;  for  what  was  it  sold  ? 

8.  A  merchant,  by  selling  40  yards  of  cloth  for 
$164,  lost  20  per  cent,  on  the  cost.  What  did  it  cost 
per  yard  ? 

9.  If  a  quart  of  brandy  cost  50  cents,  how  must  it 
be  sold  a  gill,  to  lose  4  per  cent.  ? 

10.  B  lost  5  per  cent,  by  selling  a  gallon  of  rum, 
which  cost  80  cents ;  for  what  did  he  sell  it  a  gallon  ? 

• - -»*»♦  - 

LESSON  XV. 

1.  What  principal  will,  in  4  years,  at  5  per  cent., 
amount  to  $60  ? 

Solution. — If  the  interest  of  $1  for  1  year  is  5  cents,  for  4 
years  it  is  4  times  5  cents,  or  20  cents.  Therefore,  y2^,  or  £ 
of  the  principal  equals  the  interest;  to  which  add  f,  the  prin¬ 
cipal,  and  we  have  £  of  the  principal  equal  to  the  amount,  or 
$60.  If  j  of  the  principal  is  $60,  of  the  principal  is  4  °f  $60? 
which  is  $10 ;  and  (the  principal),  is  5  times  $10,  which  are 
$50. 

2.  What  principal  will,  in  3  years,  at  6  per  cent., 
amount  to  $118  ? 

3.  What  principal  will,  in  5  years,  at  6  per  cent., 
amount  to  $130. 

4.  What  principal  will,  in  7  years,  at  5  per  cent., 
amount  to  $81  ? 

5.  What  principal  will,  in  9  years,  at  8  per  cent., 
amount  to  $86  ? 

6.  What  principal  will,  in  3£  years,  at  8  per  cent., 
amount  to  $260  ? 


DISCOUNT. 


161 


V.  What  principal  will,  in  4|  years,  at  6  per  cent., 
amount  to  $640  ? 

8.  Wliat  principal  will,  in  5^  years,  at  7  per  cent., 
amount  to  $42  ? 

9.  What  principal  will,  in  6^  years,  at  7  per  cent., 
amount  to  $87  ? 

10.  What  principal  will,  in  8§  years,  at  6  per  cent., 
amount  to  $76  ? 

Remark. — The  present  worth  of  a  debt  payable  at  some  future 
time,  without  interest,  is  such  a  sum,  as  will,  in  the  given  time, 
and  at  the  given  rate  per  cent.,  amount  to  the  debt.  Hence,  the 
present  worth  of  any  sum  of  money,  payable  at  some  future  time 
without  interest,  may  be  found  in  the  same  way  that  we  found 
the  principal ,  when  we  had  given  the  amount,  time,  and  rate 
per  cent. 

See  the  above  solution. 

11.. What  is  the  present  worth  of  $26,  due  5  years 
hence,  at  6  per  cent.  ?  Ans.  $20. 

12.  What  is  the  present  worth  of  $14,  due  8  years 
hence,  at  5  per  cent.  ? 

13.  What  is  the  present  worth  of  $110,  due  5  years 
hence,  at  5  per  cent.  ? 

14.  What  is  the  present  worth  of  $86,  due  8  years 
hence,  at  9  per  cent.  ? 

15.  What  is  the  present  worth  of  $102,  due  9  years 
hence,  at  4  per  cent.? 

16.  What  is  the  present  worth  of  $72,  due  4  years 
hence,  at  5  per  cent.  ? 

17.  VV  hat  is  the  discount  on  $46,  due  3  years  hence, 
at  5  per  cent.  ? 

Remark. — The  discount  equals  the  amount  minus  the  present 
worth. 

18.  What  is  the  discount  on  $54,  due  5  years  hence, 
at  7  per  cent.  ? 

19.  What  is  the  discount  on  $65,  due  5  years  hence, 
at  6  per  cent.  ? 

20.  What  is  the  discount  on  $93,  due  3  years  hence, 
at  8  per  cent.  ? 


14* 


162 


PERCENTAGE. 


21.  What  is  the  present  worth  of  $186,  due  4f 
years  hence,  at  5  per  cent.  ? 

22.  What  is  the  present  worth  of  $66,  due  5^  years 
hence,  at  6  per  cent.  ? 

23.  What  is  the  present  worth  of  $128,  due  4§ 
years  hence,  at  6  per  cent.  ? 

• - ^  »>  ^  >«  <>» - 

LESSON  XVI. 

1.  If  I  sell  cloth,  at  $2.50  a  yard,  and  thereby  gain 
25  per  cent.  ;  what  did  it  cost  a  yard  ? 

Solution. — If  I  gain  25  per  cent.  I  gain  \  of  the  cost;  to 
which  add  £,  the  cost,  and  I  have  f  of  the  cost  equal  to  $2.50. 
If  |  of  what  I  gave  for  it,  is  $2.50,  ^  of  the  cost  is  £  of  $2.50, 
or  50  cents ;  and  f  (the  cost)  is  4  times  50  cents,  which  are  200 
cents,  or  $2. 

2.  A  horse  was  sold  for  $38,  which  was  at  a  loss 
of  5  per  cent.  What  did  the  horse  cost  ? 

3.  If  I  sell  cloth,  at  $2.50  a  yard,  and  thereby 
gain  25  per  cent.,  how  must  I  sell  it  a  yard,  to  lose  20 
per  cent.? 

4.  If  I  sell  cloth,  at  $4.40  a  yard,  and  thereby  gain 
10  per  cent.,  how  ought  I  to  sell  it,  to  lose  25  per 
cent.  ? 

5.  If  by  selling  a  piece  of  cloth  for  $46,  I  gain  15 
per  cent.,  how  ought  I  to  have  sold  it,  to  have  lost  30 
per  cent.  ? 

6.  A  sold  his  horse  for  $105,  and  thereby  gained  5 
per  cent,  on  the  cost;  for  what  ought  he  to  have  sold 
it,  to  have  lost  10  per  cent.  ? 

7.  A  farm  was  sold  for  $495,  which  was  10  per  cent, 
less  than  what  it  was  worth  ;  for  what  ought  it  to  have 
been  sold,  to  have  received  40  per  cent,  more  than  its 
value  ? 

8.  A  mechanic  lost  20  per  cent,  on  the  cost  of  a 
wagon,  by  selling  it  for  $40  ;  for  what  ought  it  to  have 
been  sold,  to  have  gained  30  per  cent.  ? 


PERCENTAGE. 


163 


9.  A  horse  was  sold  for  $90,  which  was  10  percent, 
less  than  its  value  ;  what  would  have  been  the  gain 
per  cent.,  if  it  had  been  sold  for  $120? 

10.  A  farm  was  sold  for  $690,  which  was  8  per 
cent,  less  than  its  value ;  what  would  have  been  the 
gain  per  cent.,  if  it  had  been  sold  for  $850  ? 

11.  A  book  was  sold  for  90  cents,  which  was  10 
per  cent,  less  than  its  value ;  what  would  have  been 
the  gain  per  cent.,  if  it  had  been  sold  for  $1.50? 

12.  A  man  sold  two  watches,  at  $12  each;  on  one 
he  gained  50  per  cent.,  and  on  the  other  he  lost  50  per 
cent.  Did  he  gain  or  lose  by  the  bargain,  and  how 
much  ? 

13.  An  individual  sold  two  gold  pencils,  at  $6 
apiece ;  on  one  he  gained  20  per  cent.,  and  on  the 
other  he  lost  20  per  cent.  Did  he  gain  or  lose,  and 
how  much  ? 

14.  A  farmer  sold  two  horses  at  $210  apiece  ;  for 
one  he  received  25  per  cent,  more  than  its  value,  and 
for  the  other  25  per  cent,  less  than  its  value.  Did  he 
gain  or  lose  by  the  bargain,  and  how  much  ? 

15.  A  merchant  sold  a  quantity  of  cloth  for  $280, 
and  by  so  doing  lost  60  per  cent. ;  he  then  sold  an¬ 
other  quantity  for  $80,  and  thereby  gained  60  per 
cent.  Did  he  gain  or  lose  by  the  operation  and  how 
much  ? 

— - — — - ■ 

LESSON  XVII. 

1.  An  individual  was  ordered  to  collect  $190,  and 
his  own  fee,  which  is  to  be  5  per  cent,  on  all  the 
money  collected.  How  much  should  he  receive  ? 

Solution. — He  is  to  receive  5  per  cent,  or  T|7  or  of  all 
he  collects.  |£,  all  he  collects,  minus  A,  his  f®e,  equals  4,y  of 
all  he  collects,  or  $190,  the  amount  he  is  to  pay  his  employer. 
If  of  what  he  collects  equals  $19-0,  is  -fg  of  $190,  which 


164  MISCELLANEOUS  QUESTIONS. 

is  $10;  and  (what  lie  collects)  is  20  times  $10,  or  $200. 
Therefore  he  must  receive  $200  — $190  =  $10. 

2.  How  much  ought  xk  to  receive  for  collecting  $90 
and  his  own  fee,  of  10  per  cent,  on  all  he  collects  ? 

3.  What  amount  ot  money  will  be  sufficient  to  pay 
a  debt  of  $38  and  the  collector’s  fee,  which  is  5  per 

•  cent,  on  all  the  money  collected  ? 

4.  IIow  much  cider  must  that  man  mate  to  bring 
away  15  barrels,  after  the  o'wner  of  the  mill  receives 
16|  per  cent,  of  all  he  has  made? 

5.  How  much  grain  must  a  farmer  take  to  mill,  that 
he  may  bring  away  the  flour  of  1  bushel,  after  the  mil¬ 
ler  has  taken  10  per  cent,  of  all  he  took  there  ? 

- <»»  4  n  » - 

MISCELLANEOUS  QUESTIONS. 

1.  At  5  per  cent,  for  4  years,  what  part  of  the  prin¬ 
cipal  equals  the  interest? 

2.  In  how  many  years,  at  4  per  cent.,  will  a  given 
principal  amount  to  the  same,  as  it  would  in  8  years, 
at  6  per  cent.  ? 

3.  At  what  per  cent,  will  a  given  principal,  in  14 
years,  amount  to  the  same,  as  it  would  in  12  years,  at 
7  per  cent.  ? 

4.  If  aV  °f  Ule  principal  equals  the  interest,  what  is 
the  rate  per  cent.  ? 

5.  The  rent  of  B’s  farm,  for  8  years  amounted  to 

of  its  value.  What  per  cent,  did  he  annually  re¬ 
ceive  on  the  value  of  his  farm?. 

6.  What  is  the  interest  of  $75,  for  5f  years,  at  6 
per  cent.  ? 

7.  What  principal  will,  in  7^  years  at  8  per  cent., 
give  $24  interest  ? 

8.  What  principal  will,  in  4  j  years,  at  5  per  cent., 
amount  to  $155  ? 

. 


MISCELLANEOUS  QUESTIONS.  165 

9.  At  what  per  cent.,  will  a  given  principal  double 
itself,  in  12-1  years  ? 

10.  The  interest  of  A’s  and  B’s  fortune,  for  8  years, 
at  5  per  cent.,  is  $420.  What  is  the  fortune  of  each, 
provided  A’s  fortune  is  twice  B’s  ? 

11.  The  interest  of  of  A’s  and  £  of  B’s  fortune, 
for  7  years  at  5  per  cent.,  is  $2100.  What  is  each  of 
their  fortunes,  provided  §  of  A’s  fortune  equals  f  of 
B’s? 

12.  B  sold  his  horse,  for  -i  of  l-i  times  what  it  cost ; 
what  did  he  lose  per  cent.  ? 

13.  What  is  the  interest  of  $540  for  4  years,  at  5 
per  cent.  ? 

14.  What  is  the  interest  of  $180,  for  5  years  and  9 
months,  at  6|  per  cent.  ? 

15.  What  principal  will  in  4  years  7  months  and 
6  days,  at  6|  per  cent.,  amount  to  $412  ? 

16.  The  interest  of  the  cost  of  B’s  horse,  sleigh  and 
wagon,  for  6  years,  at  5  per  cent.,  is  $69.  What  is 
the  cost  of  each,  provided  their  prices  are  to  each 
other  respectively,  as  -I,  §  and  f  ? 

17.  What  principal  will,  in-8  years  and  8  months, 
at  7j  per  cent.,  amount  to  $419  ? 

18.  What  principal  will,  in  5  years  9  months  and 
18  days  at  10  per  cent.,  give  $116  interest  ? 

19.  In  what  time,  will  $420,  at  5  per  cent.,  give 
$147  interest? 

20.  If  the  interest  of  $200,  for  1  year  and  6  months, 
is  $18,  what  is  the  rate  per  cent.  ? 

21.  At  what  per  cent.,  will  $500,  in  4  years  and  9 
months,  give  $190  interest? 

22.  At  what  per  cent.,  will  $500,  in  22  years  and  6 
days,  amount  to  $1821  ? 

23.  At  what  per  cent,  will  a  given  principal  double 
itself,  in  20  years  ? 

24.  In  what  time  will  a  given  principal  double 
itself,  at  12|  per  cent.  ? 


166  MISCELLANEOUS  QUESTIONS. 

25.  At  wliat  per  cent,  will  a  given  principal  double 
itself,  in  6  years  and  8  months  ? 

26.  A  horse  was  bought  for  $60,  and  sold  for  $90  ; 
what  was  the  gain  per  cent.? 

27.  A  basket  containing  39  oranges,  cost  $1.20;  how 
must  they  be  sold  apiece  to  gain  30  per  cent.? 

28.  If  1  quart  of  champagne  cost  40  cents,  how 
must  it  be  sold  a  gill  to  gain  20  per  cent.  ? 

29.  What  is  the  present  worth  of  $68,  due  10 
years  hence,  at  7  per  cent.  ? 

30.  What  is  the  discount  on  $162,  due  10  years 
and  4  months  hence,  at  6  per  cent.  ? 

31.  What  is  the  present  worth  of  $87,  due  3|  years 
hence,  at  5  per  cent.  ? 

32.  If  a  hogshead  of  molasses  containing  84  gallons 
cost  $30  ;  how  must  it  be  sold  a  gallon,  to  gain  40  per 
cent.  ? 

33.  The  money  I  have  on  interest,  in  9  years,  at 
10  per  cent.,  amounts  to  $190  ;  what  is  the  prin¬ 
cipal  ? 

34.  When  money  was  worth  6  per  cent.,  I  bought 

$400  worth  of  goods  ;  6  months  afterwards  I  sold  them, 
and  gained  10  per  cent,  on  the  cost.  How  much  did 
I  gain  ?  Ans.  $28. 

3  5.  A  speculator  bought  a  horse  for  $36,  and 
sold  it  for  25  per  cent.,  more  than  he  gave  for  it ; 
which,  however,  was  10  per  cent.,  less  than  what  he 
asked  for  it.  How  much  did  he  ask  for  the  horse  ? 

36.  A  gentleman  being  asked  how  much  money  he 
had  on  interest,  replied,  that  it  instead  of  6  per  cent, 
he  should  receive  10  per  cent.,  he  would  receive  $268 
interest  more  than  he  then  did.  How  much  money 
had  he  on  interest? 

37.  A  merchant  bought  broadcloth  for  $1.20  a  yard 
and  sold  it  for  33 t  per  cent,  more  than  he  gave  for  it ; 
which,  however,  was  33^  per  cent,  less  than  his  marked 
price  for  it.  How  much  was  his  marked  price  per 
yard  ? 


MISCELLANEOUS  QUESTIONS.  167 

38.  A  merchant  sold  a  quantity  of  cloth  for  $120, 
and  by  so  doing  gained  50  per  cent.  He  then  sold 
another  quantity,  for  $120,  and  thereby  lost  50  per 
cent.  Did  he  gain  or  lose  by  the  bargain,  and  how 
much  ? 

39.  B  sold  a  horse  for  $60,  and  gained  20  per  cent. 
He  then  sold  another  horse  for  $60,  and  lost  60  per 
cent.  Did  he  gain  or  lose,  and  how  much  ? 

40.  The  interest  on  li  times  A’s,  and  f  of  B’s  for¬ 
tune,  for  8  years,  at  5  per  cent.,  is  $520.  What  is  the 
fortune  of  each,  provided  li  times  A’s  fortune,  equals 
f  of  B’s  ? 

41.  |  of  D’s  fortune  added  to  f  of  E’s,  which  is  3 
times  |  of  D’s,  being  put  on  interest  for  8  years,  at  5 
per  cent.,  gives  $800  interest.  What  is  the  fortune  of 
each  ? 

42.  The  interest  of  A’s,  B’s,  and  C’s  fortune,  for  5 
years,  at  8  per  cent.,  is  $1040.  What  is  the  fortune  of 
each,  provided  they  are  to  each  other  as  and  £  ? 

43.  The  interest,  of  A’s,  B’s,  and  C’s  fortune,  for  5± 
years,  at  6  per  cent,  is  $800.  W  hat  is  each  of  their 
fortunes,  provided  B’s,  is  twice  A’s  ;  and  B’s  and  C’s 
are  equal? 

44.  A’s  fortune  added  to  |-  of  B’s,  which  is  to  A’s 
as  2  to  3,  being  put  on  interest  for  6  years,  at  4  per 
cent.,  amounts  to  $124.  What  is  the  fortune  of 
each  ? 

45.  D’s  money  added  to  4  times  E’s,  which  is  equal 
to  D’s,  being  on  interest  for  10  years,  at  5  per  cent., 
amounts  to  $3000.  What  was  each  of  their  fortunes  ? 

46.  The  sum  of  f  of  A’s  4-  }  of  B’s  money,  being 
on  interest  for  8  years,  at  5  per  cent.,  amounts  to 
$2100.  Provided  \  of  B’s  money  is  twice  f  of  A’s  ; 
how  much  money  has  each  ? 

47.  |  of  the  cost  of  C’s  house,  increased  by  §  of  the 
cost  of  bis  farm,  being  placed  on  interest  for  10  years, 
at  7  per  cent.,  amounts  to  $17000.  What  is  the  cost 


168  MISCELLANEOUS  QUESTIONS. 

of  each,  if  |  of  the  cost  of  the  house  is  only  i  of  f 
of  the  cost  of  the  farm  ?. 

48.  If  f  of  A’s  fortune  ip  2  years  and  4  months,  at 
6  per  cent.,  amounts  to  $570  ;  what  is  his  whole 
fortune  ? 

49.  The  sum  of  A’s,  and  B’s  fortune  in  4  years  and 
8  months,  at  6  per  cent.,  amounts  to  $256.  What 
was  each  of  their  fortunes,  provided  §  of  A’s  fortune 
equals  B’s  ? 

50.  The  interest  for  5  years,  at  6  per  cent.,  on  §  of 
the  money  Morgan  owes  is  $180;  and  the  interest  for 
the  same  time  and  rate  per  cent.,  on  §  of  the  money 
due  him  is  $120.  IIow  much  has  Morgan  after  pay¬ 
ing  his  debts  ? 

51.  The  money  John  paid  for  a  sheep,  a  cow,  and  a 
horse,  in  8  years,  at  10  per  cent.,  would  give  such  an 
interest,  as  would  in  f  as  long,  at  -i  as  great  a  per  cent., 
amount  to  $104  ;  how  much  did  he  pay  for  each,  pro¬ 
vided  the  sheep  cost  \  as  much  as  the  cow,  and  the 
cow  ±  as  much  as  the  horse? 

52.  The  interest  of  the  sum  of  \  of  Simpson’s,  f  of 
Eyer’s,  and  ^  of  Homer’s  fortune  for  3  years  7  months 
and  6  days,  at  10  per  cent,  is  such  as  will  in  the  same 
time,  at  \  the  rate  per  cent,  amount  to  $531.  What 
is  the  fortune  of  each,  provided  times  Homer’s  part 
of  the  principal  equals  £  of  Eyer’s,  and  T7^  of  Eyer’s 
part  of  the  principal  equals  |  of  Simpson’s  ? 

53.  The  interest  of  the  sum  of  i  of  A’s,  and  |  of 
B’s  fortune,  for  a  certain  time,  at  2  per  cent.,  was  to 
this  sum  as  9  to  250.  And  the  amount  of  this  interest 
for  25  times  as  long,  at  10  times  as  great  a  per  cent., 
was  $180.  What  was  each  of  their  fortunes,  provided, 
A’s  fortune  was  to  B’s  as  1  to  3  ?  And  how  long  was 
the  first  on  interest  ? 

Remark. — Since  the  interest  was  to  the  principal  as  9  to  250, 

of  the  principal  equals  the  interest.  Hence,  1  year  9  months 
and  18  days  is  the  time  required, 


QUESTIONS,  QUERIES,  AND  PUZZLES, 


FOB 


PUPILS  AT  HOME. 


« *■ 


1.  A  hound  is  in  pursuit  of  a  fox  that  is  10  rods  ahead  of  him, 
and  while  the  hound  runs  10  rods  the  fox  runs  1  rod,  (i  e. 
while  the  hound  runs  a  certain  distance,  the  fox  runs  one-tenth 
of  that  distance.)  Will  the  hound  overtake  the  fox  ?  The  con¬ 
ditions  remaining  the  same,  what  is  the  greatest  distance  they 
can  run  ? 

2.  A  hound  is  in  pursuit  of  a  fox  that  is  10  rods  ahead  of 
him,  and  while  the  fox  runs  1  rod  the  hound  runs  10  rods.  How 
far  will  the  hound  run  before  he  overtakes  the  fox  ? 

3.  Place  four  5’s  in  such  a  position  that  they  shall  equal  6J. 

4.  A  boy  was  sent  to  a  spring  with  a  5,  and  a  3  quart  meas¬ 
ure  to  procure  exactly  4  quarts  of  water.  How  did  he  measure 
it? 

6.  What  is  the  difference  between  twice  25,  and  twice  5  and 
20? 

6.  A  man  had  9  pigs  and  put  them  in  four  pens,  with  an  odd 
number  of  pigs  in  each  pen.  How  did  he  divide  them  ? 

7.  Two  men  have  an  8  gallon  cask  full  of  wine,  which  they 
desire  to  divide  equally  between  them.  How  can  they  effect  this 
division,  provided  the  only  measures  they  have  are  a  5  gallon 
cask  and  a  3  gallon  cask? 

8.  Place  four  2’s  in  such  a  manner  that  they  shall  exactly 
equal  23. 

9.  Place  9  apples  in  10  rows  so  that  each  row  shall  contain 
3  apples. 

10.  A  squirrel  finding  9  ears  of  corn  in  a  box,  took  from  it 
daily,  3  ears ;  how  many  days  was  he  in  removing  the  corn  from 
the  box  ? 

11.  If  from  six  you  take  IX,  and  from  IX  you  take  ten  ;  and 
if  fifty  from  forty  be  taken,  there  will  then  just  half  a  dozen 
remain. 


15 


170  QUESTIONS  AND  PUZZLES. 


12.  Edward,  Maria,  and  their  mother  went  to  market.  Ed¬ 
ward  had  60  apples  and  sold  them,  at  2  for  1  cent ;  Maria  had 
60  apples  and  sold  them,  at  3  for  1  cent.  Their  mother  had 
120  apples  and  sold  them,  at  the  rate  of  5  for  2  cents.  Which 
received  the  most,  the  children  or  the  mother,  and  why  ? 

13.  A  gentleman  desiring  to  see  an  inmate  of  a  prison,  was 
asked  by  the  keeper  whether  he  was  related  to  the  culprit,  re¬ 
plied  :  “  brothers  and  sisters  have  I  none,  but  his  father  is  my 
father’s  son.”  What  relation  was  the  gentleman  to  the  prisoner  ? 

14.  A  man  having  a  fox,  a  goose,  and  a  peck  of  corn,  was 
desirous  of  crossing  a  river.  He  could  take  only  one  across  at 
a  time,  and  if  he  left  the  fox  and  goose,  while  he  took  the  com 
over,  the  fox  would  kill  the  goose ;  but  if  he  left  the  goose  and 
corn,  the  goose  would  eat  the  corn.  How  shall  he  get  them  all 
safely  across  the  river  ? 

15.  A  snail  wants  to  get  up  a  wall  20  feet  in  height,  during 
the  day  it  climbs  5  feet,  but  slips  back  4  feet  every  night ;  how 
many  days  would  it  take  to  reach  the  top  ? 

16.  A  man  purchased  a  hat  for  $5,  and  handed  the  mer¬ 
chant  a  $50  bill  to  pay  for  it;  the  merchant  being  unable  to 
make  the  change,  sent  the  bill  to  a  broker,  got  it  changed,  and 
then  gave  the  man  who  bought  the  hat  $45.  The  broker,  after 
the  purchaser  of  the  hat  had  gone,  discovered  that  the  bill  was 
counterfeit  and,  therefore,  returned  it  to  the  merchant  and  re¬ 
ceived  $50  good  money.  How  much  did  the  merchant  lose  by 
the  operation  ? 

17.  Place  ten  pennies  in  a  row,  then  carry  one  over  two, 
leaving  it  upon  the  third,  and  continue  doing  this  until  the  ten 
pennies  occupy  only  live  places  with  two  in  each  place. 

18.  Two  boys  laid  a  wager  as  to  which  could  lift  the  most 
One  lifted  ninety-nine  pounds,  and  the  other  a  hundred,  and 
icon.  How  many  pounds  did  both  lift  ? 

19.  A  frog,  at  the  bottom  of  a  well  10  feet  deep,  ascends  3 
feet  every  jump.  How  many  jumps  must  he  take  to  get  out  ? 

20.  A  drover  being  asked  how  many  horses  he  had  replied, 
“  my  horses  together  have  twenty  fore  legs  how  many  horses 
had  he  ? 

21.  Write  12  in  such  a  manner,  that  you  can  show  its  half  to 
be  7. 

22.  “I  am  constrained  to  plant  a  grove 
To  please  the  lady  that  I  love, 

This  ample  grove  is  to  compose, 

Nineteen  trees  in  nine  straight  rows ; 

Five  trees  in  each  row  I  must  place. 

Or  I  shall  never  see  her  face.” 


QUESTIONS  AND  PUZZLES.  l7l 


23.  Do  the  waters  of  the  Mississippi  river  flow  up  hill? 

24.  If  a  man  should  start  from  the  city  of  New  York,  at 
12  o’clock  on  Monday,  and  travel  directly  west  for  24  hours,  at 
the  rate  of  15  degrees  an  hour,  it  is  evident  he  would  then  have 
reached  New  York  again.  It  was  Monday  12  o’clock  when  he 
started,  and  has  been  midday  to  him  during  his  journey ;  (the 
sun  being  in  his  meridian,)  on  his  return  to  New  York  City  it  is 
Tuesday,  12  o’clock ;  at  what  point  on  his  journey  did  it  change 
from  Monday  to  Tuesday  noon  ? 

25.  Arrange  in  a  square  the  numbers  from  1  to  16,  in  such  a 
manner  that  they  shall  amount  to  the 
same  in  each  column,  whether  added 
perpendicularly,  horizontally,  diagonally, 
or  taking  any  four  of  the  numbers  in 
the  form  of  a  square. 


1 

12 

6 

15 

5 

13 

3 

10 

11 

2 

16 

5 

14 

7 

9 

4 

Magic  Squares — An  East  India  Puzzle. 
Puzzle. — Take  any  odd  number  whatever — square  it. 


and 


write  the  series  of  figures  from  one  to  the  square  of  the  number 
taken,  in  a  square  whose  side  is  indicated  by  the  number  taken, 
in  such  a  manner  that  the  figures  added  horizontally,  perpen¬ 
dicularly,  or  diagonally,  shall  equal  the  same  sum. 

Example. — Take  the  number  5, — its  square  is  25, — write  the 
figures  from  1  to  25  in  a  square  made  up  of  twenty-five  smaller 
squares  in  such  a  manner  that,  added  perpendicularly,  horizon¬ 
tally,  or  diagonally,  the  sum  shall  be  the  same,  that  is,  one-fifth 
of  the  sum  of  the  series  of  numbers,  1  to  25; — and  so  of  the 
numbers  7,  9,  11,  etc. 

Pule. — Begin  by  placing  1  in  the  middle  square  at  the  top, 
then,  in  filling  up,  observe  these  directions  according  to  the  posi¬ 
tion  of  the  square  just  filled,  viz. :  Proceed  diagonally  upward 
to  the  right,  or  if  you  can  not  do  this  go  to  the  square  on  the 
opposite  side  of  the  parallelogram  in  the  next  line  at  the  right, 
or  next  line  above ;  or  if  you  can  not  do  this,  take  the  square 
immediately  below. 

These  figures  can  be  varied  in 
at  least  four  different  ways.  If 
the  number  7  be  taken,  they  can 
be  varied  six  different  ways;  if 
9  be  taken,  they  can  be  varied 
eight  different  ways,  perhaps 
more, 


17 

24 

1 

8 

15 

23 

5 

7 

14 

•  16 

4 

6 

13 

20 

22 

10 

12 

19 

21 

3 

11 

18 

25 

2 

9 

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